Geometry 11.2 ‐ Surface areas of Prisms and Cylinders A. Prisms

Geometry 11.2 ‐ Surface areas of Prisms and Cylinders A. Prisms

Geometry
11.2 ‐ Surface areas of Prisms and Cylinders
A. Prisms ‐ any solid figure where bases (top and bottom) are parallel and congruent.
• Lateral Faces ‐ faces that make up the sides of the prism
• Altitude ‐ the height of the prism
• Right Prism ‐ any prism where the lateral face intersects the base at a right angle, or the lateral faces are rectangles. We will work with right prisms. • Lateral Area ‐ the sum of the areas of the lateral faces
• Surface Area ‐ the total area of all faces of the prism
B. Theorem 11 ‐ 1 (lateral and surface areas of a prism)
1. Lateral area is the perimeter of the base times the height
LA = P ∙ H
2. Surface area is the sum of the lateral area and twice the area of the base
SA = LA + 2B
Mar 15­4:17 PM
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May 3­10:05 AM
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C. Find the lateral area and surface area of the following prisms
3. Trapezoidal Prism
2. Triangular Prism
1. Rectangular Prism
20 in
7 mm
5 in
12 ft
25 mm
10 mm
17 in
14 in
7 ft
8 ft
Mar 15­5:38 PM
3
D. Cylinders ‐ a solid with congruent circular bases
Right Cylinder ‐ the segment joining the centers of the circular bases •
are altitudes (we will work with right cylinders)
Surface Area: twice the area of the base plus the circumference times •
the height
SA = 2πr2 + 2πrh
Mar 15­5:40 PM
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E. Examples. Find the surface area of the following cylinders. 5.
4. 12 cm
6.
3.5 in
9 cm
8 in
14 mm
11 mm
Mar 15­5:41 PM
5
F. Applications/Word Problems
7. Find the height of a cylinder with a radius of 6.5 cm and SA of 592.19 cm2
8. The SA of a cylinder = 100πm2. If r = h, find r and h.
Mar 15­5:42 PM
6
9. Two cylindrical cans of soup sell for the same price. One has a diameter of 6 in and a height of 5 in while the other can has a diameter of 5 in and a height of 6 in. Which can is the better buy?
Mar 15­5:43 PM
7
11.2 HW (p. 611) numbers 1 ­ 10 all
Apr 2­11:50 AM
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