Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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 p. 3 m3 167 cm3

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

Learn to find the surface area of prisms and cylinders.

Vocabulary surface area lateral face lateral surface

Surface area is the sum of the areas of all surfaces of a figure 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.

Additional Example 1: Finding Surface Area Find the surface area of each figure to the nearest tenth. Use 3.14 for p. A. S = 2pr2 + 2prh = 2p(42) + 2p(4)(6) = 80p in2  251.2 in2 B. S = 2B + Ph = 2( • 8 • 3) + (18)(10) 1 2 = 204 ft2

Check It Out: Example 1 Find the surface area of each figure to the nearest tenth. Use 3.14 for p. 15 cm A. S = 2pr2 + 2prh 3 cm = 2p(152) + 2p(15)(3) = 540p in2  1695.6 cm2 7 cm 7 cm 6 cm B. S = 2B + Ph = 2( • 7 • 6) + (21)(10) 1 2 10 cm 7 cm = 252 cm2

Additional 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.

Check It Out: Example 2 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. Original Dimensions Double the Height Double the Radius S = 2pr2 + 2pr(2h) S = 2pr² + 2prh S = 2pr2 + 2p(2r)h = 2p(3)2 + 2p(3)(4) = 2p(3)2 + 2p(3)(2) = 2p(6) 2 + 2p(3)(2) = 30p in2 ≈ 94.2 in2 = 42p in2 ≈ 131.88 in2 = 84p in2 ≈ 263.76 in2 They would not have the same effect. Doubling the radius would increase the surface area more than doubling the height.

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. L = 2rh = 2(3.8)(11.2) Diameter = 7.6 cm, so r = 3.8 cm. ≈ 267.3 cm2

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? S = 2r2 + 2rh The diameter is 6 ft, so r = 3 ft. = 2(32) + 2(3)(12) ≈ 282.6 ft2 Move the decimal point 2 places to the left to divide by 100. ≈ 2.826 gal

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 14

Lesson Quiz Find the surface area of each figure to the nearest tenth. Use 3.14 for p. 1. the triangular prism 2. the cylinder 360 cm2 320.3 in2 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? 84 in2

Lesson Quiz for Student Response Systems 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 16

Lesson Quiz for Student Response Systems 2. Identify the surface area of the cylinder rounded to the nearest tenth. Use 3.14 for p. A. 421.3 in2 B. 454.7 in2 C. 477.3 in2 D. 520.2 in2 17

Lesson Quiz for Student Response Systems 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 18