Measurement Strand - Swampscott High School

Transcription

MEASUREMENT STRAND
1.
(edited by Monteiro)
Grade 10 | Mathematics | Multiple Choice | 2005 | Question 40
Reporting Category: Measurement Standard(s): 10.M.1
How many square feet of carpeting are needed to cover the floor of the room represented by the drawing
below? Note that the shaded region is to be left uncovered to leave space for the construction of a built-in
trophy case with a rectangular base.
A. 125 sq. ft.
B. 243 sq. ft.
C. 273 sq. ft.
D. 303 sq. ft.
MEASUREMENT STRAND
2.
Tiffany wants to calculate the volume of her globe. The globe is in the shape of a sphere, as represented by
the picture below. She measured the circumference of the globe along the equator to be 24 inches.
Which of the following measures is closest to the volume of Tiffany’s globe?
A. 46 cubic inches
B. 61 cubic inches
C. 183 cubic inches
D. 234 cubic inches
MEASUREMENT STRAND
3. Grade 10 | Mathematics | Multiple Choice | 2005 | Question 24
What is h, the height of the triangle represented below, if its area is 58.5 square centimeters?
A. 13 cm
B. 18 cm
C. 26 cm
D. 39 cm
MEASUREMENT STRAND
What is the area of the parallelogram represented below?
A. 32 cm2
B. 24 cm2
C. 16 cm2
D. 12 cm2
MEASUREMENT STRAND
5.
A right circular cylindrical can is 6 inches high, and the area of its top is 36 square inches. What is the
minimum number of square inches of construction paper it would take to cover the lateral surface of this can?
A. 72 sq. in.
B. 72
sq. in.
C. 432 sq. in.
D. 432
sq. in.
MEASUREMENT STRAND
What is h, the height of the parallelogram represented below, if its area is 91 square centimeters?
A. 7 cm
B. 9 cm
C. 11 cm
D. 15 cm
MEASUREMENT STRAND
7.
The wheels on Bill’s bicycle each have a radius of 35 centimeters. Which of the following is closest to the
distance the bicycle moves along the ground in one complete revolution of the wheels?
A. 35 cm
B. 55 cm
C. 110 cm
D. 220 cm
MEASUREMENT STRAND
Jennifer keeps a box under her bed to store clothes. The box is in the shape
of a rectangular prism as shown in the figure below.
Jennifer’s sister, Molly, made a box that had the same height as Jennifer’s box. Molly, however, realized that
she could triple the length and double the width and it would still fit under her bed.
What is the ratio of the volume of Molly’s box to the volume of Jennifer’s box?
A. 6:1
B. 12:1
C. 36:1
D. 216:1
MEASUREMENT STRAND
The trapezoid pictured below has the measurements shown.
Which measure is closest to the perimeter of the trapezoid?
A. 41 inches
B. 59 inches
C. 64 inches
D. 66 inches
MEASUREMENT STRAND
The right cylinder and right cone shown below have the same radius and volume. The cylinder has a height
of 12 inches.
What is h, the height of the cone?
A. 18 inches
B. 24 inches
C. 36 inches
D. 42 inches
MEASUREMENT STRAND
A landing pad for a helicopter is in the shape of a circle with a radius of 7 meters. Which of the following is
closest to the area of the landing pad?
A. 44 square meters
B. 154 square meters
C. 205 square meters
D. 308 square meters
MEASUREMENT STRAND
A glass lampshade is in the shape of a right circular cone with radius, r, and slant height, , as given below.
r = 7.5 inches
= 12.5 inches
Which of the following is closest to the lateral surface area of the lampshade?
A. 236 sq. in.
B. 295 sq. in.
C. 412 sq. in.
D. 589 sq. in.
MEASUREMENT STRAND
Circle O is inscribed in square EFGH, as shown below.
The circumference of circle O is 20 centimeters. Which of the following is closest to the perimeter of square
EFGH?
A. 24 cm
B. 25.5 cm
C. 27 cm
D. 28.5 cm
MEASUREMENT STRAND
Rectangle ABCD is similar to rectangle EFGH.
•
•
The length of each side of rectangle EFGH is 2.4 times the length of the corresponding side of
rectangle ABCD.
The perimeter of rectangle ABCD is 120 feet.
What is the perimeter of rectangle EFGH?
A. 288 feet
B. 345.6 feet
C. 576 feet
D. 691.2 feet
MEASUREMENT STRAND
Kevin used snowballs in the shape of a sphere to build a snowman. The radius of the largest snowball was
1.5 times the radius of the smallest snowball.
How many times greater was the volume of the largest snowball than the volume of the smallest snowball?
A. 7.065
B. 6.28
C. 3.375
D. 2.25
MEASUREMENT STRAND
The diagram below shows a right rectangular prism that is 7 inches wide, 12 inches long, and 4 inches high.
What is the volume, in cubic inches, of the prism?
A. 152
B. 184
C. 320
D. 336
MEASUREMENT STRAND
Manuel is using a small paper rectangle and a large paper rectangle for an art project.
•
The length of the small rectangle is half the length of the large rectangle.
•
The width of the small rectangle is half the width of the large rectangle.
The area of the small rectangle is how many times the area of the large rectangle?
A.
B.
C.
D.
MEASUREMENT STRAND
Each of two different-sized boxes is in the shape of a right rectangular prism. The volume of the larger box is
4 times the volume of the smaller box. The dimensions of the smaller box are represented below.
•
length: l
•
width: w
•
height: h
Which of the following could represent the dimensions of the larger box?
A. l, 4w, 4h
B. 2l, 2w, h
C. 2l, 2w, 4h
D. 4l, 4w, 4h
MEASUREMENT STRAND
The circumference of Sophie’s circular flower garden is 75 feet. Which of the following is closest to the
diameter of her flower garden?
A. 24 feet
B. 12 feet
C. 10 feet
D.
5 feet
MEASUREMENT STRAND
An international basketball court has a region called the free-throw lane, shown as the shaded part in the
diagram below.
•
The free-throw lane is shaped like an isosceles trapezoid.
•
A semicircle, shown as the unshaded part in the diagram, is attached to the shorter base of the
trapezoid.
•
The radius of the semicircle is 1.8 meters.
Based on the dimensions in the diagram, what is the area of the shaded free-throw lane?
A. 22.62 square meters
B. 27.84 square meters
C. 34.80 square meters
D. 55.68 square meters
MEASUREMENT STRAND
Parallelogram PQRS is shown below.
Some of the dimensions of the parallelogram are as follows:
•
•
•
QR = 7 cm
RS = 5 cm
QT = 6.5 cm
What is the area of the parallelogram?
A. 24 cm2
B. 32.5 cm2
C. 35 cm2
D. 45.5 cm2
MEASUREMENT STRAND
An artist carved a sphere out of stone. The radius of the sphere is 0.93 meter.
Which of the following is closest to the volume of the sphere?
A.
3.37 m3
B.
3.62 m3
C.
10.11 m3
D.
11.69 m3
MEASUREMENT STRAND
Two containers in the shape of right circular cylinders are equal in height. The radius of the larger
container is 3 times the radius of the smaller container.
The volume of the larger container is how many times the volume of the smaller container?
A.
3
B.
6
C.
9
D.
27
MEASUREMENT STRAND
A trapezoid and its dimensions are shown below.
What is the area of the trapezoid?
A.
60 sq. in.
B.
168 sq. in.
C.
210 sq. in.
D.
336 sq. in.
MEASUREMENT STRAND
Which of the following is closest to the circumference, in inches, of a circle that has a diameter of 12
inches?
A.
18.84
B.
37.68
C.
75.36
D. 113.04
MEASUREMENT STRAND
The diagram below shows a parallelogram and its dimensions.
Which of the following has an area equal to the area of the parallelogram?
A.
B.
C.
D.
MEASUREMENT STRAND
The diagram below shows the dimensions of a garden.
In the diagram, all intersecting line segments intersect at right angles. What is the area of the garden?
A. 1200 sq. ft.
B. 1300 sq. ft.
C. 1500 sq. ft.
D. 1800 sq. ft.
MEASUREMENT STRAND
A mechanic has two pieces of sandpaper of different sizes. Each piece is in the shape of a circle. The radius
of the larger circle is 4 times the radius of the smaller circle.
The area of the larger circle is how many times the area of the smaller circle?
A.
2
B.
4
C.
8
D. 16
MEASUREMENT STRAND
Ms. Burke correctly weighed a tomato to the nearest ounce and recorded the weight. The weight she
recorded was 13 ounces.
What is the least possible actual weight of the tomato?
A. 12.0 ounces
B. 12.5 ounces
C. 13.0 ounces
D. 13.4 ounces
MEASUREMENT STRAND
30.
Grade 10 | Mathematics | Open Response | 2005 | Question 21
Carla can use 100 square feet of floor space in her school’s gymnasium, in any way she chooses, to set up
computer stations for a science fair. She has chosen to use floor space in the shape of a rectangle, with
dimensions that are whole numbers.
a. Draw all possible rectangles with an area of 100 square feet and whole-number dimensions. Your
drawings do not have to be to scale, but you must label the dimensions on each drawing.
b. Carla plans to buy a length of rope to surround her floor space. Which rectangle that you drew in part
a. has the smallest perimeter and will thus require the least amount of rope? Show or explain how
you got your answer.
c.
To set up her computer stations, Carla will subdivide her rectangular floor space into small rectangles
that each measure 2 feet by 4 feet.
o Using the rectangle you chose in part b. as Carla’s floor space, what is the maximum number
of these small rectangles that she can create?
o To support your answer, sketch the rectangle from part b. subdivided into the maximum
number of these small rectangles.
o Explain how you know your answer is correct.
MEASUREMENT STRAND
31.
A glass containing water is in the shape of a right circular cylinder with a radius of 3 centimeters. The height
of the water in the glass is 10 centimeters.
a. What is the volume of the water in the glass? Be sure to include units of measure in your answer.
Show or explain how you obtained your answer.
b. Five spherical marbles of equal size are dropped into the glass. The water in the glass rises to a
height of 11 centimeters. What is the increase in the volume of the contents of the glass? Be sure to
include units of measure in your answer. Show or explain how you obtained your answer.
c.
What is the volume of one of the marbles? Be sure to include units of measure in your answer. Show
or explain how you obtained your answer.
d. What is the radius of one of the marbles? Be sure to include units of measure in your answer. Show
or explain how you obtained your answer.
MEASUREMENT STRAND
32.
A can shaped like a right circular cylinder holds 2 pounds of coffee and has a diameter
of 6 inches and a height of
inches.
a. What is the total surface area of the coffee can? Show or explain how you obtained your answer.
b. What is the volume of the can? Show or explain how you obtained your answer.
c. A conical scoop is used to remove coffee from the can and place it into a coffee maker. The scoop
has a 1-inch diameter and a 2-inch height. If one level scoop is used to make each cup of coffee, how
many cups of coffee can be made from a full 2-pound can of coffee? Show or explain how you obtained
your answer.
MEASUREMENT STRAND
33.
Grade 10 | Mathematics | Open Response
|
2006
|
Question
41
The rear window of Alex's van is shaped like a trapezoid with an upper base measuring 36 inches, a lower
base measuring 48 inches, and a height of 21 inches. An 18-inch rear window wiper clears a 150° sector of a
circle on the rear window, as shown in the diagram below.
a) What is the area, in square inches, of the entire trapezoidal rear window? Show or explain how you
got your answer.
b) What fractional part of a complete circle is cleared on the rear window by the 18-inch wiper? Show or
explain how you got your answer.
c) What is the area, in square inches, of the part of the rear window that is cleared by the wiper? Show
or explain how you got your answer.
d) What percent of the area of the entire rear window is cleared by the wiper? Show or explain how you
got your answer.
MEASUREMENT STRAND
34.
A water dunking tank at a carnival is in the shape of a right circular cylinder. Its height is 5 feet, and the
radius of each base is 3 feet, as shown in the picture below.
1. What is the lateral surface area, in square feet, of the tank? Show your work.
2. On the first day of the carnival, the dunking tank was filled with water to a height of 4 feet. What was
the volume, in cubic feet, of the water in the tank on the first day of the carnival? Show your work.
At the end of the second day of the carnival, some water was drained from the tank. The volume of water
drained was 35.3 cubic feet.
3. Using your answer from part (b), determine the height, in feet, of the water remaining in the tank after
the water was drained at the end of the second day. Show your work.
The water that was drained from the tank was poured into containers, each in the shape of a right
rectangular prism. Each container was 2 feet in length, 1.5 feet in width, and 3 feet in height.
4. What was the least number of containers needed to hold all the water that was drained at the end of
the second day? Show your work.
MEASUREMENT STRAND
35.
Zachary made a right square pyramid out of plaster for an art project. Each side of his pyramid's base
measured 8 inches. The slant height,
shown below.
, of his pyramid measured 5 inches. A diagram of his pyramid is
a. What is the area, in square inches, of the base of Zachary's pyramid? Show your work.
b. What is the total surface area, in square inches, of Zachary's pyramid? Show your work.
c. What is h, the height, in inches, of Zachary's pyramid? Show or explain how you got your answer.
d.
Using the height you determined in part (c), what is the volume, in cubic inches, of Zachary's pyramid?
Show your work.
MEASUREMENT STRAND
36. Grade 10 | Mathematics | Open Response | 2009 | Question 42
Ralph’s company makes doormats. Each doormat is in the shape of a semicircle, as shown in the diagram
below.
Each doormat has two parts: a rough fiber interior and a vinyl border.
•
•
The rough fiber interior is in the shape of a semicircle with a diameter of 28 inches.
The vinyl border has a uniform width of 4 inches. The shaded part in the diagram represents the vinyl
border.
a) What is the radius, in inches, of the rough fiber interior? Show or explain how you got your answer.
b) What is the radius, in inches, of the entire doormat? Show or explain how you got your answer.
c) What is the area, in square inches, of the rough fiber interior? Show or explain how you got your
answer.
d) What is the area, in square inches, of the vinyl border? Show or explain how you got your answer.
MEASUREMENT STRAND
37.
Grade 10 | Mathematics | Short Answer | 2005 | Question 15
Trapezoid ABCD shown below has bases measuring 6 inches and 10 inches and a height of x inches.
Square EFGH shown below has sides measuring x inches. The trapezoid and the square have equal areas.
What is the value of x, in inches?
MEASUREMENT STRAND
38. Grade 10 | Mathematics | Short Answer | 2004 | Question 16
The length of the hypotenuse of a right triangle is 13 centimeters, and the length of one leg is 12 centimeters.
What is the area of the triangle?
MEASUREMENT STRAND
In the figure below, A, C, and D are collinear, the area of ΔABC is 24 square centimeters, and the area of
ΔABD is 40 square centimeters. If the measure of
is 8 centimeters, what is the length of
?
MEASUREMENT STRAND
The volume of Anand's cube is 8 cubic centimeters. What is the total surface area, in square centimeters, of
his cube?
MEASUREMENT STRAND
Rectangle KLMN and its dimensions are shown below. Point P lies on
What is the area, in square centimeters, of
NPM?
.
MEASUREMENT STRAND
42.
Hannah's garden is in the shape of a parallelogram. A diagram representing her garden is shown below.
Hannah needs to know the area of the garden in order to buy the correct amount of fertilizer. Based on the
dimensions in the diagram, what is the area, in square yards, of Hannah's garden?
MEASUREMENT STRAND
The diagram below shows parallelogram MNPQ and one of its dimensions.
The perimeter of parallelogram MNPQ is 54 centimeters. What is the length, in centimeters, of NP ?
MEASUREMENT STRAND
The cone shown below has a radius of 8 feet and a height of 12 feet.
What is the volume of the cone?
A. 32
cubic feet
B. 256
cubic feet
C. 374
cubic feet
D. 768
cubic feet
MEASUREMENT STRAND
A company packages breakfast cereal in the two sizes of right cylindrical containers shown below. The
containers are similar in shape.
How many cubic inches does the large container hold?
A. 90
cubic inches
B. 135
cubic inches
C. 360
cubic inches
D. 540
cubic inches
MEASUREMENT STRAND
The rectangle shown below has a width of 2.5 feet and a perimeter of 13 feet.
What is the area of the rectangle?
A. 4 square feet
B. 8 square feet
C. 10 square feet
D. 10.5 square feet
MEASUREMENT STRAND
What is the effect on the circumference of a circle if the circle's radius is doubled?
A. The circumference is multiplied by 2.
B. The circumference is multiplied by 4.
C. The circumference is multiplied by 8.
D. The circumference stays the same.
MEASUREMENT STRAND
Which expression represents the area of the shaded portion of the square below?
2
A. n –
n
2
B. n – 2 n
2
2
C. n – ( n )
D.
2
n
n –(
2
)2
MEASUREMENT STRAND
Each ride on the Ferris wheel consists of 6 rotations. If the length of each of the spokes from the center of the
wheel to a seat is t feet, how far will each passenger travel during a ride?
A. 6t feet
B. 6 t feet
C. 12t feet
D. 12 t feet
MEASUREMENT STRAND
CanCorp is determining the cost of labels for new cans with the dimensions shown below.
The label for each can will wrap around the side of the can with no overlap. What is the approximate area of
one label?
2
A. 1847 cm
2
B. 264 cm
2
C. 528 cm
2
D. 924 cm
MEASUREMENT STRAND
Use the graphic below to answer question 22.
Students at Viking High School decide to have T-shirts made with a blue "V" inside a gold rectangle as
shown in the diagram above.
The costs are as follows:
•
•
•
plain T-shirt $8.50
blue coloring $0.02 per square inch
gold coloring $0.04 per square inch
a. What is the area of the blue "V" in the diagram above? Show your work.
b. Explain how you can determine the area that will be colored gold.
c. What will be the total cost for each T-shirt shown above? Show your work.
MEASUREMENT STRAND
52.
Geoffrey is building a patio. The floor of his patio will be made of bricks. The diagram below shows the shape of
each brick.
Geoffrey can combine two bricks side-by-side to make different shapes. An example of one combination of two
bricks is shown below.
What combination of two bricks would have the smallest base perimeter? Draw this combination in the space
below.
MEASUREMENT STRAND
Reporting Category: Measurement Standard(s): 10.M.2 - Given the formula, find the lateral
area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones.
A sphere has a volume of
centimeters, of the sphere?
A.
B.
C.
D.
500
π cubic centimeters. What is the total surface area, in square
3
MEASUREMENT STRAND
Reporting Category: Measurement Standard(s): 10.M.1 - Calculate perimeter,
circumference, and area of common geometric figures such as parallelograms, trapezoids,
circles, and triangles.
A circle has a diameter of 18 feet. Which of the following is closest to the circumference of the circle?
A. 28.3 feet
B. 56.5 feet
C. 113.1 feet
D. 254.5 feet
MEASUREMENT STRAND
circumference, and area of common geometric figures such as parallelograms, trapezoids,
circles, and triangles.
A. 30 cm2
B. 36 cm2
C. 60 cm2
D. 72 cm2
MEASUREMENT STRAND
Reporting Category: Measurement Standard(s): 10.M.3 - Relate changes in the
measurement of one attribute of an object to changes in other attributes, e.g., how
changing the radius or height of a cylinder affects its surface area
Marcos has two cubes of different sizes. The length of each edge of the larger cube is 2 times the length of
each edge of the smaller cube. The volume of the larger cube is how many times the volume of the smaller
cube?
A. 4
B. 6
C. 8
D. 16
MEASUREMENT STRAND
Reporting Category: Measurement Standard(s): 10.M.1 - Calculate perimeter, circumference,
and area of common geometric figures such as parallelograms, trapezoids, circles, and
triangles.
A. 38 sq. in.
B. 48 sq. in.
C. 66 sq. in.
D. 88 sq. in.
MEASUREMENT STRAND
Reporting Category: Measurement Standard(s): 10.M.2 - Given the formula, find the lateral area,
surface area, and volume of prisms, pyramids, spheres, cylinders, and cones.
A storage cabinet is in the shape of a rectangular prism. The diagram below shows the storage cabinet and
its dimensions.
What is the volume of the cabinet?
A. 11 cubic feet
B. 21 cubic feet
C. 27 cubic feet
D. 63 cubic feet
MEASUREMENT STRAND
triangles.
A stage floor is composed of a rectangle and an isosceles trapezoid. The diagram below shows the
stage floor and some of its dimensions.
What is the perimeter of the stage floor?
A. 110 ft.
B. 145 ft.
C. 1000 ft.
D. 1375 ft.
MEASUREMENT STRAND
triangles.
The radius of a circle is 12 centimeters. What is the area, in square centimeters, of the circle?
A.
B.
C.
D.
MEASUREMENT STRAND
Reporting Category: Measurement Standard(s): 10.M.1 - Calculate perimeter, circumference, and area of
common geometric figures such as parallelograms, trapezoids, circles, and triangles.
Abby drew
and
, as shown in the diagram below.
The figure in the diagram has the following properties:
•
Point H lies on
.
•
The length of
is 8 inches.
•
The length of
is 10 inches.
What is the area of the shaded triangle,
A. 80 sq. in.
B. 64 sq. in.
C. 48 sq. in.
D. 40 sq. in.
?
MEASUREMENT STRAND
Reporting Category: Measurement Standard(s): 10.M.3 - Relate changes in the measurement
of one attribute of an object to changes in other attributes, e.g., how changing the radius or
height of a cylinder affects its surf
A pizza restaurant uses small pans and large pans.
•
•
Each pan is in the shape of a circle.
The area of the large pan is 9 times the area of the small pan.
The radius of the large pan is how many times the radius of the small pan?
A. 3
B. 6
C. 9
D. 27
MEASUREMENT STRAND
A can of chili and a can of soup are both in the shape of a right circular cylinder.
•
•
The cans are of equal height.
The radius of the can of chili is 2 times the radius of the can of soup.
The volume of the can of chili is how many times the volume of the can of soup?
A. 2
B. 4
C. 6
D. 8
MEASUREMENT STRAND
Nadia has a box shaped like a right rectangular prism.
•
•
•
The length of the box is 5 feet.
The height of the box is 2 feet.
The volume of the box is 30 cubic feet.
What is the width of the box?
A. 3 feet
B. 12 feet
C. 20 feet
D. 23 feet
MEASUREMENT STRAND
triangles.
A circle has an area of 16π square centimeters. What is the circumference of the circle?
A. 32π centimeters
B. 16π centimeters
C. 8π centimeters
D. 4π centimeters
MEASUREMENT STRAND
Reporting Category: Measurement Standard(s): 10.M.2 - Given the formula, find the lateral area, surface
area, and volume of prisms, pyramids, spheres, cylinders, and cones.
A cube has a volume of 27 cubic inches. What is the total surface area of the cube?
A. 18 square inches
B. 36 square inches
C. 54 square inches
D. 72 square inches
MEASUREMENT STRAND
The diagram below shows a right circular cone and its measurements.
Which of the following is closest to the lateral surface area of the cone?
A. 151 sq. ft.
B. 188 sq. ft.
C. 377 sq. ft.
D. 480 sq. ft.
MEASUREMENT STRAND
68.
A powdered drink mix container is in the shape of a right circular cylinder. The dimensions of the
container are shown below.
Which of the following is closest to the volume of the container?
A. 188 cubic inches
B. 283 cubic inches
C. 471 cubic inches
D. 1131 cubic inches
MEASUREMENT STRAND
A shipping container is in the shape of a rectangular prism. The dimensions of the shipping container
are shown in the diagram below.
Which of the following is closest to the total surface area of the container?
A. 6.09 m2
B. 10.20 m2
C. 12.94 m2
D. 20.41 m2
MEASUREMENT STRAND
triangles.
The area of a right triangle is 24 square units. Which of the following sets of numbers could represent the
side lengths, in units, of the right triangle?
A. 3, 8, and 9
B. 4, 6, and 8
C. 6, 8, and 10
D. 4, 12, and 15
MEASUREMENT STRAND
triangles.
A trapezoid and some of its dimensions are shown below.
The area of the trapezoid is 100 square centimeters. What is the height of the trapezoid?
A. 2 cm
B. 4 cm
C. 8 cm
D. 10 cm
MEASUREMENT STRAND
triangles.
Which of the following is closest to the circumference of a circle that has a diameter of 8 inches?
A. 13 inches
B. 25 inches
C. 50 inches
D. 64 inches
MEASUREMENT STRAND
triangles.
Some of the dimensions of a driveway are shown in the diagram below.
What is the area of the driveway?
A. 1600 sq. yd.
B. 1700 sq. yd.
C. 2200 sq. yd.
D. 2400 sq. yd.
MEASUREMENT STRAND
Two different-sized right square pyramids have bases of equal area.
•
•
The altitude of the smaller pyramid is h.
The altitude of the larger pyramid is 2h.
The volume of the larger pyramid is how many times the volume of the smaller pyramid?
A. 8
B. 4
C. 3
D. 2
MEASUREMENT STRAND
A circular dinner plate has a radius
3
times the radius of a circular salad plate. The area of the
2
dinner plate is how many times the area of the salad plate?
A.
B.
C.
D.
MEASUREMENT STRAND
76.
Reporting Category: Measurement Standard(s): 10.M.2 - Given the formula, find the
lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and
cones.
Paloma bought a block of wax in the shape of a right rectangular prism. The diagram below shows the block
and its dimensions.
a)
What is the volume, in cubic centimeters, of the block of wax? Show your work.
Paloma melted the block of wax to make candles. The first candle she made is in the shape of a right circular
cylinder. The diagram below represents the candle and its dimensions.
b)
What is the volume, in cubic centimeters, of the first candle? Show your work.
c)
Paloma wanted to make a second candle in the shape of a right square pyramid with a side length of
10 centimeters and a height of 12 centimeters. Show that she does not have enough remaining wax to make
this candle.
d)
Paloma decided instead to make the second candle in the shape of a right square pyramid with a side
length of 8 centimeters. If she uses all the remaining wax, what will be the height, in centimeters, of the
candle? Show your work.
MEASUREMENT STRAND
77.
area, surface area, and volume of prisms, pyramids, spheres, cylinders, and s.
A company manufactures solid glass spheres. Each sphere has a radius of 2 inches and is packed in a gift box
shaped like a cube. The box is small enough so that each side of the box touches the sphere.
a)
What is the length, in inches, of each edge of the box? Show or explain how you got your answer.
b)
What is the volume, in cubic inches, of the box? Show your work.
Material is added to the spaces around the glass spheres in the boxes to prevent breakage.
c)
work.
What is the volume, in cubic inches, of the space inside the box but outside the sphere? Show your
The company wants to pack multiple cube-shaped boxes into large boxes for shipping. Each large box is in the
shape of a right rectangular prism and has a length of 24 inches, a width of 20 inches, and a height of 16
inches.
d)
What is the maximum number of cube-shaped boxes that can fit inside a large box? Show your work.
MEASUREMENT STRAND
A company manufactures different sizes of foam balls. Each foam ball is in the shape of a sphere.
a)
A small foam ball has a radius of 4 inches. What is the volume, in cubic inches, of the small
foam ball? Show or explain how you got your answer.
b)
A medium foam ball has a radius of 6 inches. What is the surface area, in square inches, of
the medium foam ball? Show or explain how you got your answer.
A large foam ball has a radius of 12 inches. The company manufactures an extra-large foam ball
that has a surface area equal to twice the surface area of the large foam ball.
c)
What is the radius, to the nearest inch, of the extra-large foam ball? Show or explain how
MEASUREMENT STRAND
79.
A monument in the shape of a right square pyramid is located in a park. The park is in the shape of a
rectangle. The measurements of the monument and the park are shown in the diagram below.
a)
What is the area, in square meters, of the base of the monument? Show or explain how you
got your answer.
b)
What is the area, in square meters, of the park, not including the base of the monument?
Show or explain how you got your answer.
c)
What is the lateral surface area, in square meters, of the monument? Show or explain how
The height of the monument is 24 meters.
d)
What is the volume, in cubic meters, of the monument? Show or explain how you got your
answer.
MEASUREMENT STRAND
80.
Terrell designed the original external fuel tank for a spacecraft. The tank is in the shape of a right
circular cylinder. The diagram below shows the tank's dimensions.
a)
What is the radius, in feet, of the tank? Show or explain how you got your answer.
b)
What is the total amount of fuel, in cubic feet, that the tank holds when it is full? Show or
explain how you got your answer.
Terrell is planning the design for a new tank that will also be in the shape of a right circular cylinder.
When the new tank is full, it must hold 2 times the amount of fuel that the original tank held. Terrell is
investigating two design options, which he calls Design P and Design Q.
c)
For Design P, the radius of the new tank would be the same as the radius of the original
tank. What should be the height, in feet, of the new tank in Design P? Show or explain how you got
your answer.
d)
For Design Q, the height of the new tank would be the same as the height of the original
tank. What should be the radius, in feet, of the new tank in Design Q? Show or explain how you got
your answer.
MEASUREMENT STRAND
circumference, and area of common geometric figures such as parallelograms,
trapezoids, circles, and triangles.
Yoshi is designing a monument that has a triangular base. He drew
monument, as shown in the diagram below.
to represent the base of the
Based on the measurements in the diagram, what is the area, in square meters, of
?
MEASUREMENT STRAND
The diagram below shows a right circular cone with a radius of 5 centimeters and a slant height of
10 centimeters.
What is the lateral surface area, in square centimeters, of the cone? (You may leave your answer in
terms of π.)
MEASUREMENT STRAND
The diagram below shows a right square pyramid.
Based on the dimensions in the diagram, what is the lateral surface area, in square centimeters, of
the pyramid?
MEASUREMENT STRAND
triangles.
The diagram below shows a triangle and some of its measurements.
What is the area, in square feet, of the triangle?
MEASUREMENT STRAND
Answer Key
1) B
11) B
21)
31)
41)
51)
61) D
71) C
81) 48
2) D
12) B
22)
32)
42)
52)
62) A
72) B
82) 50π
3) A
13) B
23)
33)
43)
53) C
63) B
73) B
83) 320
cm2
4) A
14) A
24)
34)
44)
54) B
64) A
74) D
84) 6
5) B
15) C
25)
35)
45)
55) C
65) C
75) B
85)
6) A
16) D
26)
36)
46)
56) C
66) C
76) OR
86)
7) D
17) C
27)
37)
47)
57) C
67) B
77) OR
87)
8) A
18) B
28)
38)
48)
58) C
68) B
78) OR
88)
9) C
19) A
29)
39)
49)
59) B
69) D
79) OR
89)
10) C
20) B
30)
40)
50)
60) C
70) C
80) OR
90)
MEASUREMENT STRAND
111)
121)
131)
141)
151)
161)
171)
181)
191)
201)
112)
122)
132)
142)
152)
162)
172)
182)
192)
202)
113)
123)
133)
143)
153)
163)
173)
183)
193)
203)
114)
124)
134)
144)
154)
164)
174)
184)
194)
204)
115)
125)
135)
145)
155)
165)
175)
185)
195)
205)
116)
126)
136)
146)
156)
166)
176)
186)
196)
206)
117)
127)
137)
147)
157)
167)
177)
187)
197)
207)
118)
128)
138)
148)
158)
168)
178)
188)
198)
208)
119)
129)
139)
149)
159)
169)
179)
189)
199)
209)
120)
130)
140)
150)
160)
170)
180)
190)
200)
210)

Measurement Strand - Swampscott High School

Transcription

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