Lesson 8.6Surface Areas of Prisms

and Cylinderspp. 341-347

Lesson 8.6Surface Areas of Prisms

and Cylinderspp. 341-347

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.

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.

Remember that cylinders and cones with polygonal bases

are called prisms and pyramids, respectively.

Remember that cylinders and cones with polygonal bases

are called prisms and pyramids, respectively.

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.

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.

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

8 in.8 in.

4 in.4 in.

12 in.12 in.

8 in8 in 8 in8 in4 in4 in 4 in4 in

12 in12 in

8 in8 in

8 in8 in

4 in4 in

4 in4 in

24 in24 in

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.

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.

EXAMPLE Find the surface area for the circular cylinder. EXAMPLE Find the surface area for the circular cylinder.

66

99

S = L + 2B

S = cH + 2B

S = 2rH + 2r2

S = 2(6)(9) + 2(36)S = 108 + 72S = 180 ≈ 565 square units

S = L + 2B

S = cH + 2B

S = 2rH + 2r2

S = 2(6)(9) + 2(36)S = 108 + 72S = 180 ≈ 565 square units

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

8 in8 in

12 in12 in

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

88

88

12121616

Homeworkpp. 345-347Homeworkpp. 345-347

►A. Exercises1. Find the lateral surface area of the

right prism if the base is a square.

►A. Exercises1. Find the lateral surface area of the

right prism if the base is a square.

1212

2525

L = pHL = 4(12)(25)L = 1200 units2

L = pHL = 4(12)(25)L = 1200 units2

►A. ExercisesFind the lateral surface area and total surface area of the following figure.

3.

►A. ExercisesFind the lateral surface area and total surface area of the following figure.

3.

553.53.5

88

L = pHL = 5(5)(8)L = 200 units2

L = pHL = 5(5)(8)L = 200 units2

B = ½apB = ½(3.5)(25)B = 43.75 units2

B = ½apB = ½(3.5)(25)B = 43.75 units2

►A. ExercisesFind the lateral surface area and total surface area of the following figure.

3.

►A. ExercisesFind the lateral surface area and total surface area of the following figure.

3.

553.53.5

88

S = L + 2BS = 200 + 2(43.75)S = 287.5 units2

S = L + 2BS = 200 + 2(43.75)S = 287.5 units2

►A. ExercisesFind the lateral surface area and total surface area of the following figure.

5.

►A. ExercisesFind the lateral surface area and total surface area of the following figure.

5.

88

2323

L = pHL = 6(8)(23)L = 1104 units2

L = pHL = 6(8)(23)L = 1104 units2

B = ½apB = ½apB = ½(4 3)(48)B = ½(4 3)(48)B = 96 3 units2B = 96 3 units2

►A. ExercisesFind the lateral surface area and total surface area of the following figure.

5.

►A. ExercisesFind the lateral surface area and total surface area of the following figure.

5. S = L + 2B

88

2323

S = 1104 + 2(96 3)S = 1104 + 2(96 3)S = 1104 + 192 3S = 1104 + 192 3S ≈ 1436.6 units2S ≈ 1436.6 units2

L = pHL = (106)(34)L = 3604 units2

L = pHL = (106)(34)L = 3604 units2

B = ½h(b1+b2)B = ½(9)(18+38)B = 252 units2

B = ½h(b1+b2)B = ½(9)(18+38)B = 252 units2

3821

34

1829

9

►A. ExercisesFind the lateral surface area and total surface area of the following figure.

7.

►A. ExercisesFind the lateral surface area and total surface area of the following figure.

7.

3821

34

1829

9

►A. ExercisesFind the lateral surface area and total surface area of the following figure.

7.

►A. ExercisesFind the lateral surface area and total surface area of the following figure.

7. S = L + 2BS = 3604 + 2(252)S = 3604 + 504 S = 4108 units2

S = L + 2BS = 3604 + 2(252)S = 3604 + 504 S = 4108 units2

►B. Exercises13. The surface area of a cube is 1350 sq.

inches. Find the dimensions of this cube.

►B. Exercises13. The surface area of a cube is 1350 sq.

inches. Find the dimensions of this cube.

L = pHL = 4s(s)L = 4s2

L = pHL = 4s(s)L = 4s2

B = s2B = s2

S = L + 2BS = 4s2 + 2(s2)S = 6s2

1350 = 6s2

s2 = 225s = 15 inches

S = L + 2BS = 4s2 + 2(s2)S = 6s2

1350 = 6s2

s2 = 225s = 15 inches

►B. Exercises15. Find the lateral area of a right circular

cylinder whose diameter is 10 3 feet and whose height is 27 feet.

►B. Exercises15. Find the lateral area of a right circular

cylinder whose diameter is 10 3 feet and whose height is 27 feet.

10 3

27 L = 270 3L = 270 3

L = 10 3 (27)L = 10 3 (27)

L = cHL = cH

L ≈ 1469.2 feet2L ≈ 1469.2 feet2

►C. Exercises20. Find the surface area of the napkin

ring.

►C. Exercises20. Find the surface area of the napkin

ring.

diam.4 cmdiam.4 cm

3 cm3 cm0.4 cm0.4 cm

■ Cumulative ReviewDefine each term.■ Cumulative ReviewDefine each term.

24. circle25. tangent26. supplementary angles27. congruent angles28. circumcenter

24. circle25. tangent26. supplementary angles27. congruent angles28. circumcenter