10 5 Surface Area of Pyramids and Cones

10 -5 Surface Area of Pyramids and Cones Preview Warm Up California Standards Lesson Presentation Holt CA Course 1

10 -5 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 Holt CA Course 1

10 -5 Surface Area of Pyramids and Cones California Standards Extension of MG 2. 1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic threedimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. Holt CA Course 1

10 -5 Surface Area of Pyramids and Cones Vocabulary slant height regular pyramid right cone Holt CA Course 1

10 -5 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 vertex passes through the center of the base. Holt CA Course 1

10 -5 Surface Area of Pyramids and Cones Holt CA Course 1

10 -5 Surface Area of Pyramids and Cones Additional Example 1: Finding Surface Area Find the surface area of the 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 S=B+ Holt CA Course 1

10 -5 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 Holt CA Course 1 ft 2 18 ft 7 ft

10 -5 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 only the slant height would have the same effect on the surface area as tripling only the radius. Use 3. 14 for p. They would not have the same effect. Tripling the radius would increase the surface area more than tripling the slant height. Holt CA Course 1

10 -5 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 only the slant height would have the same effect on the surface area as tripling only the radius. Use the 3. 14 for p. Original Dimensions S = r 2 + rl Triple the Slant Height S = r 2 + r(3 l) Triple the Radius S = (3 r)2 + (3 r)l = (4. 5)2 + (4. 5)(2) = (4. 5)2 + (4. 5)(6) = (13. 5)2 + (13. 5)(2) = 29. 25 in 2 91. 8 in 2 = 47. 25 in 2 148. 4 in 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. Holt CA Course 1

10 -5 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 Pythagorean Theorem 102 + 242 = l 2 l = 26 L = rl Lateral surface area = (10)(26) 816. 8 mm 2 Holt CA Course 1

10 -5 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 92 + 122 = l 2 l = 15 L = rl Pythagorean Theorem Lateral surface area 12 in. = (9)(15) 424. 1 in 2 Holt CA Course 1 9 in.

10 -5 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 Holt CA Course 1

10 -5 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. Holt CA Course 1