1. How do you Calculate the Surface Area of Prisms & Cylinders?
9.2
Essential Question:
How do you Calculate the Surface Area of Prisms & Cylinders?

2. Surface Area Sum of all the areas of the faces of a polyhedron
i.e. Calculate the area of each face using the formulas for area of polygon and then add them together.

3. Find the surface area of the rectangular prism.
Example 1
Use the Net of a Prism
Find the surface area of the rectangular prism. 15 40 24 24 40 15 3

4. Find the surface area of the rectangular prism.
Example 1
Use the Net of a Prism
Find the surface area of the rectangular prism.
SOLUTION
Add the areas of all the rectangles that form the faces of the prism.
Congruent Faces
Dimensions
Area of Face
Left face and right face
8 in. by 5 in.
8  5 = 40 in.2
Front face and back face
8 in. by 3 in.
8  3 = 24 in.2
Top face and bottom face
3 in. by 5 in.
3  5 = 15 in.2 4

5. Add the areas of all the faces to get the surface area.
Example 1
Use the Net of a Prism
Add the areas of all the faces to get the surface area.
S =
Add the area of all six faces.
= 158
Simplify.
ANSWER
The surface area of the prism is 158 square inches. 5

6. Find the surface area of the prism.
Example 2
Find Surface Area of a Prism
Find the surface area of the prism. 6

7. Find the surface area of the prism.
Example 2
Find Surface Area of a Prism
Find the surface area of the prism.
Triangles: 2
A = ½ bh
= ½ (3)(4)
= 6
2 Triangles = 6 times 2
= 12
Rectangle
A = (4)(2)=8
A = 3 * 2 = 6
A = 5 * 2 = 10
= 24
SA =
= 36 m2 7

8. Surface Area of a Prism SA = 2BA + PBh
Where B = area of the base and P = the perimeter of the base

9. Find the surface area of the prism.
Example 2
Find Surface Area of a Prism
Find the surface area of the prism.
SOLUTION 1.
Find the area of a triangular base.
BA = 1 2
· 4 · 3 = 2 · 3 = 6 2.
Find the perimeter of a base.
PB = = 12 3.
Find the height of the prism. In the diagram, h = 2. 9

10. Use the formula for surface area of a prism.
Example 2
Find Surface Area of a Prism 4.
Use the formula for surface area of a prism.
S = 2BA + PBh
Formula for the surface area of a prism
= 2 · · 2
Substitute 6 for B, 12 for P, and 2 for h. =
Multiply.
= 36
Add.
ANSWER
The surface area of the prism is 36 square meters. 10

11. Checkpoint
Find Surface Area of Prisms 2.
Find the surface area. 1. 3.

12. Find the surface area of the prism.
Checkpoint
Find Surface Area of Prisms
Find the surface area of the prism. 1.
ANSWER
72 in.2 2.
ANSWER
236 ft2 3.
ANSWER
144 cm2

13. SA = 2πr2 + 2πrh SA = 2BA + PBh Surface Area of A Cylinder
SA = 2B + Ph

14. The surface area is about 132 square feet.
Example 3
Find Surface Area of a Cylinder
Find the surface area of the cylinder. Round your answer to the nearest whole number.
SOLUTION
The radius of the base is 3 feet and the height 4 feet. Use these values in the formula for surface area of a cylinder.
S = 2πr2 + 2πrh
Write the formula for surface area.
= 2π(32) + 2π(3)(4)
Substitute 3 for r, and 4 for h.
= 18π + 24π
Simplify.
= 42π
Add.
≈ 132
Multiply.
ANSWER
The surface area is about 132 square feet. 14

15. Checkpoint
Find Surface Area of Cylinders
Find the area described. Round your answer to the nearest whole number. 5.
surface area 4.
surface area 6.
lateral area

16. Checkpoint
Find Surface Area of Cylinders
Find the area described. Round your answer to the nearest whole number. 4.
surface area
ANSWER
151 in.2 5.
surface area
ANSWER
603 ft2 6.
lateral area
ANSWER
13 m2

17. Review:
Tell whether the solid is a polyhedron. If so, identify the shape of the bases. Then name the solid. 1.
The solid is not a polyhedron.
ANSWER 2.
The solid is a polyhedron with congruent triangular bases in parallel planes, so it is a triangular prism.
ANSWER

18. Name the polyhedron. Count the number of faces and edges and then list the congruent faces and congruent edges. 3.
ANSWER
pentagonal pyramid; 6 faces, 10 edges; congruent faces: ∆PJN  ∆NJM  ∆MJL  ∆LJK  ∆KJP; congruent edges:  NJ PJ KP LJ MJ LK NM PN KJ , ML

19. Worksheet 9.2A