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Quiz Find the volume of each figure to the nearest tenth.Use 3.14 for p. 1. the triangular pyramid 2. the cone Find the surface area of each figure to the nearest tenth. Use 3.14 for p. 3. the triangular prism 4. the cylinder Surface and Area of Pyramids and Cones 6.9 Pre-Algebra 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 m2 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 p. 1186.9 cm2 Learn to find the surface area of pyramids and cones. Vocabulary slant height regular pyramid right cone The slant height of a pyramid or cone is measured along its lateral surface. Right cone Regular Pyramid The base of a regular 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. Example: Finding Surface Area Find the surface area of each figure 1 Pl 2 1 = (2.4 • 2.4) + (9.6)(3) 2 = 20.16 ft2 A. S = B + B. S = pr2 + prl = p(32) + p(3)(6) = 27p 84.8 cm2 Try This Find the surface area of each figure. 1 Pl 2 1 = (3 • 3) + (12)(5) 2 = 39 m2 5m A. S = B + 3m 3m B. S = pr2 + prl = p(72) + p(7)(18) = 175p 549.5 ft2 18 ft 7 ft Example: 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. Try This 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 = pr2 + pr(3l) S = pr2 + prl = p(4.5)2 + p(4.5)(2) = 29.25p in2 Triple the Slant Height 91.8 in2 = p(4.5)2 + p(4.5)(6) = 47.25p in2 148.4 in2 Triple the Radius S = p(3r)2 + p(3r)l = p(13.5)2 + p(13.5)(2) = 209.25p in2 657.0 in2 They would not have the same effect. Tripling the radius would increase the surface area more than tripling the height. Example: 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? a2 + b2 = l2 102 + 262 = l2 l 27.9 L = prl Pythagorean Theorem Lateral surface area = p(10)(27.9) 876.1 mm2 Try This A road construction cone is almost a full cone. With the given dimensions, what is the lateral surface area of the cone? a2 + b2 = l2 Pythagorean Theorem 42 + 122 = l2 l 12.65 L = prl Lateral surface area = p(4)(12.65) 158.9 in2 12 in. 4 in. Lesson Quiz: Part 1 Find the surface area of each figure to the nearest tenth. Use 3.14 for p. 1. the triangular pyramid 6.2 m2 2. the cone 175.8 in2 Lesson Quiz: Part 2 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.