Surface Area of Prisms and Cylinders9-7

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

Surface Area of Prisms and Cylinders9-7

Warm Up

1. A triangular pyramid has a base area of 1.2 m2 and a height of 7.5 m. What is the volume of the pyramid?

2. A cone has a radius of 4 cm and a height of 10 cm. What is the volume of the cone to the nearest cubic centimeter? Use 3.14 for .

3 m3

167 cm3

Surface Area of Prisms and Cylinders9-7

Problem of the Day

An ice cream cone is filled halfway to the top. The radius of the filled part is half the radius at the top. What fraction of the cone’s volume is filled?1

8

Surface Area of Prisms and Cylinders9-7

Prep for MA.8.G.5.1 …Convert units of measure between different measurement systems…and dimensions including…area…and derived units to solve problems.Rev MA.7.G.2.1

Sunshine State Standards

Surface Area of Prisms and Cylinders9-7

Vocabulary

surface arealateral facelateral surface

Surface Area of Prisms and Cylinders9-7

Surface area is the sum of the areas of all surfaces of a figure. The lateral faces of a prism are parallelograms that connect the bases. The lateral surface of a cylinder is the curved surface.

Surface Area of Prisms and Cylinders9-7

Surface Area of Prisms and Cylinders9-7

A. S = 2r2 + 2rh

= 2(42) + 2(4)(6)

= 80 in2 251.2 in2

B. S = 2B + Ph

= 204 ft2

= 2( • 8 • 3) + (18)(10)12

Additional Example 1: Finding Surface Area

Find the surface area of each figure to the nearest tenth. Use 3.14 for .

Surface Area of Prisms and Cylinders9-7

A. S = 2r2 + 2rh

= 2(152) + 2(15)(3)

= 540 in2 1695.6 cm2

B. S = 2B + Ph

= 252 cm2

= 2( • 7 • 6) + (21)(10)12

Check It Out: Example 1

15 cm

3 cm

7 cm7 cm

7 cm10 cm

6 cm

Find the surface area of each figure to the nearest tenth. Use 3.14 for .

Surface Area of Prisms and Cylinders9-7Additional Example 2: Exploring the Effects of Changing

Dimensions A cylinder has diameter 8 in. and height 3 in. Explain whether tripling the height would have the same effect on the surface area as tripling the radius.

They would not have the same effect. Tripling the radius would increase the surface area more than tripling the height.

Surface Area of Prisms and Cylinders9-7

Check It Out: Example 2

Original Dimensions Double the Height Double the Radius

S = 2r² + 2rh

= 2(3)2 + 2(3)(2)

= 30in2 ≈ 94.2 in2

S = 2r2 + 2r(2h)

= 2(3)2 + 2(3)(4)

= 42in2 ≈ 131.88 in2

S = 2r2 + 2(2r)h

= 2(6) 2 + 2(3)(2)

= 84in2 ≈ 263.76 in2

A cylinder has diameter 6 in. and height 2 in. Explain whether doubling the height would have the same effect on the surface area as doubling the radius.

They would not have the same effect. Doubling the radius would increase the surface area more than doubling the height.

Surface Area of Prisms and Cylinders9-7

Additional Example 3: Application

A cylindrical soup can is 7.6 cm in diameter and 11.2 cm tall. What is the area of the label that covers the side of the can?

Only the lateral surface needs to be covered.

Diameter = 7.6 cm, so r = 3.8 cm.

L = 2rh

= 2(3.8)(11.2)

≈ 267.3 cm2

Surface Area of Prisms and Cylinders9-7

Check It Out: Example 3

A cylindrical storage tank that is 6 ft in diameter and 12 ft tall needs to be painted. The paint will cover 100 square feet per gallon. How many gallons will it take to paint the tank?

The diameter is 6 ft, so r = 3 ft.

S = 2r2 + 2rh

= 2(32) + 2(3)(12)

≈ 282.6 ft2 Move the decimal point 2 places to the left to divide by 100.≈ 2.826 gal

Surface Area of Prisms and Cylinders9-7

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Surface Area of Prisms and Cylinders9-7

3. All outer surfaces of a box are covered with gold foil, except the bottom. The box measures 6 in. long, 4 in. wide, and 3 in. high. How much gold foil was used?

Lesson QuizFind the surface area of each figure to the nearest tenth. Use 3.14 for .

1. the triangular prism

2. the cylinder320.3 in2

360 cm2

84 in2

Surface Area of Prisms and Cylinders9-7

1. Identify the surface area of the triangular prism rounded to the nearest tenth.

A. 156 cm2

B. 162 cm2

C. 166 cm2

D. 172 cm2

Lesson Quiz for Student Response Systems

Surface Area of Prisms and Cylinders9-7

2. Identify the surface area of the cylinder rounded to the nearest tenth. Use 3.14 for .

A. 421.3 in2

B. 454.7 in2

C. 477.3 in2

D. 520.2 in2

Lesson Quiz for Student Response Systems

Surface Area of Prisms and Cylinders9-7

3. All the outer surfaces of a box are covered with leather except the top and bottom. The box measures 5 inches long, 3 inches wide, and 2 inches high. How much leather is used?

A. 16 in2

B. 30 in2

C. 32 in2

D. 40 in2

Lesson Quiz for Student Response Systems