Area ofof Pyramids and Cones 8 8 Surface

Area ofof Pyramids and Cones 8 -8 Surface Area Pyramids and Cones 8 -8 Surface Warm Up Problem of the Day Lesson Presentation Course 33

8 -8 Surface Area of Pyramids and Cones Warm Up 1. A rectangular prism is 0. 6 m by 0. 4 m by 1. 0 m. What is the surface area? 2. 48 m 2 2. A cylindrical can has a diameter of 14 cm and a height of 20 cm. What is the surface area to the nearest tenth? Use 3. 14 for . 1186. 9 cm 2 Course 3

8 -8 Surface Area of Pyramids and Cones Problem of the Day Sandy is building a model of a pyramid with a hexagonal base. If she uses a toothpick for each edge, how many toothpicks will she need? 12 Course 3

8 -8 Surface Area of Pyramids and Cones Learn to find the surface area of pyramids and cones. Course 3

8 -8 Surface Area of Pyramids and Cones Vocabulary slant height regular pyramid right cone Course 3

8 -8 Surface Area of Pyramids and Cones The slant height of a pyramid or cone is measured along its lateral surface. Regular Pyramid The base of a regular Right cone pyramid is a regular polygon, and the lateral faces are all congruent. In a right cone, a line perpendicular to the base through the tip of the cone passes through the center of the base. Course 3

8 -8 Surface Area of Pyramids and Cones Course 3

8 -8 Surface Area of Pyramids and Cones Additional Example 1: Finding Surface Area Find the surface area of each figure to the nearest tenth. Use 3. 14 for p. 1 Pl 2 1 = (2. 4 • 2. 4) + (9. 6)(3) 2 = 20. 16 ft 2 A. S = B + B. S = pr 2 + prl = (32) + (3)(6) = 27 84. 8 cm 2 Course 3

8 -8 Surface Area of Pyramids and Cones Check It Out: Example 1 Find the surface area of each figure to the nearest tenth. Use 3. 14 for p. 5 m A. S = B + 1 Pl 2 1 = (3 • 3) + (12)(5) 2 = 39 m 2 3 m 3 m B. S = pr 2 + prl = (72) + (7)(18) = 175 549. 5 Course 3 ft 2 18 ft 7 ft

8 -8 Surface Area of Pyramids and Cones Additional Example 2: Exploring the Effects of Changing Dimensions A cone has diameter 8 in. and slant height 3 in. Explain whether tripling the slant 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 slant height. Course 3

8 -8 Surface Area of Pyramids and Cones Check It Out: Example 2 A cone has diameter 9 in. and a slant height 2 in. Explain whether tripling the slant height would have the same effect on the surface area as tripling the radius. Original Dimensions S = r 2 + r(3 l) S = r 2 + rl = (4. 5)2 + (4. 5)(2) = 29. 25 in 2 Triple the Slant Height 91. 8 in 2 = (4. 5)2 + (4. 5)(6) = 47. 25 in 2 148. 4 in 2 Triple the Radius S = (3 r)2 + (3 r)l = (13. 5)2 + (13. 5)(2) = 209. 25 in 2 657. 0 in 2 They would not have the same effect. Tripling the radius would increase the surface area more than tripling the height. Course 3

8 -8 Surface Area of Pyramids and Cones Additional Example 3: Application The upper portion of an hourglass is approximately an inverted cone with the given dimensions. What is the lateral surface area of the upper portion of the hourglass? a 2 + b 2 = l 2 102 + 242 = l 2 l = 26 L = rl Pythagorean Theorem 24 mm Lateral surface area = (10)(26) 816. 8 mm 2 Course 3

8 -8 Surface Area of Pyramids and Cones Check It Out: Example 3 A large road construction cone is almost a full cone. With the given dimensions, what is the lateral surface area of the cone? a 2 + b 2 = l 2 Pythagorean Theorem 92 + 122 = l 2 l = 15 L = rl 12 in. Lateral surface area = (4)(15) 188. 4 in 2 Course 3 9 in.

8 -8 Surface Area of Pyramids and Cones Lesson Quiz: Part I Find the surface area of each figure to the nearest tenth. Use 3. 14 for p. 1. the triangular pyramid 6. 2 m 2 2. the cone 175. 8 in 2 Course 3

8 -8 Surface Area of Pyramids and Cones Lesson Quiz: Part II 3. Tell whether doubling the dimensions of a cone will double the surface area. It will more than double the surface area because you square the radius to find the area of the base. Course 3