1. Surface Areas of Prisms and Cylinders
Lesson 8.6
Surface Areas of Prisms and Cylinders pp

2. Objectives:
1. To differentiate between surface area and lateral surface area of prisms and cylinders.
2. To derive and apply formulas for calculating the surface area of prisms and cylinders.

3. Remember that cylinders and cones with polygonal bases are called prisms and pyramids, respectively.

4. Theorem 8.14
The surface area of a prism is the sum of the lateral surface area and the area of the bases: S = L + 2B.
The lateral surface area of a right prism is the product of its height and the perimeter of its base: L = pH.

5. Find the lateral and total surface area of the following solid figure.

6. 8 in
4 in
24 in
12 in
8 in
4 in
8 in
4 in
4 in
8 in

7. Theorem 8.15
The surface area of a cylinder is the sum of the lateral surface area and the area of the bases: S = L + 2B.
The lateral surface area of a right cylinder is the product of its circumference and height: L = cH.

8. EXAMPLE Find the surface area for the circular cylinder.6 9
S = L + 2B
S = cH + 2B
S = 2rH + 2r2
S = 2(6)(9) + 2(36)
S = 108 + 72
S = 180 ≈ 565 square units

9. Find the lateral and total surface area of the following solid figure.

10. Find the lateral and total surface area of the following solid figure.8 12
16

11. Homework pp

12. ►A. Exercises 1. Find the lateral surface area of the
right prism if the base is a square.
L = pH
L = 4(12)(25)
L = 1200 units2 25 12

13. ►A. Exercises
Find the lateral surface area and total surface area of the following figure. 3.
L = pH
L = 5(5)(8)
L = 200 units2 8
B = ½ap
B = ½(3.5)(25)
B = units2
3.5 5

14. ►A. Exercises
Find the lateral surface area and total surface area of the following figure. 3.
S = L + 2B
S = (43.75)
S = units2 8
3.5 5

15. ►A. Exercises
Find the lateral surface area and total surface area of the following figure. 5.
L = pH
L = 6(8)(23)
L = 1104 units2 8 23
B = ½ap
B = ½(4 3)(48)
B = units2

16. ►A. Exercises
Find the lateral surface area and total surface area of the following figure. 5.
S = L + 2B 8 23
S = (96 3)
S =
S ≈ units2

17. ►A. Exercises
Find the lateral surface area and total surface area of the following figure. 7. 18
L = pH
L = (106)(34)
L = 3604 units2 29 34
B = ½h(b1+b2)
B = ½(9)(18+38)
B = 252 units2 9 21 38

18. ►A. Exercises
Find the lateral surface area and total surface area of the following figure. 7. 18
S = L + 2B
S = (252)
S =
S = 4108 units2 29 34 9 21 38

19. ►B. Exercises
13. The surface area of a cube is 1350 sq. inches. Find the dimensions of this cube.
L = pH
L = 4s(s)
L = 4s2
S = L + 2B
S = 4s2 + 2(s2)
S = 6s2
1350 = 6s2
s2 = 225
s = 15 inches
B = s2

20. ►B. Exercises
15. Find the lateral area of a right circular cylinder whose diameter is feet and whose height is 27 feet.
L = cH 27
L = 10 3 (27)
L = 270 3
10 3
L ≈ feet2

21. ►C. Exercises 20. Find the surface area of the napkin ring. 0.4 cm
diam.
4 cm
3 cm
0.4 cm

22. ■ Cumulative Review Define each term. 24. circle 25. tangent
26. supplementary angles
27. congruent angles
28. circumcenter