Holt CA Course Surface Area of Pyramids and Cones Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

Holt CA Course 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. 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  m cm 2

Holt CA Course Surface Area of Pyramids and Cones Extension of MG2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three- dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. California Standards

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

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

Holt CA Course Surface Area of Pyramids and Cones

Holt CA Course 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 . = ft 2 S = B + Pl 1212 = ( ) + (9.6)(3) 1212

Holt CA Course Surface Area of Pyramids and Cones Check It Out! Example 1 = (3 3) + (12)(5) 1212 B. S = r 2 + rl = 39 m 2 = (7 2 ) + (7)(18) = 175  ft 2 5 m 3 m 7 ft 18 ft A. S = B + Pl 1212 Find the surface area of each figure to the nearest tenth. Use 3.14 for .

Holt CA Course 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 . They would not have the same effect. Tripling the radius would increase the surface area more than tripling the slant height.

Holt CA Course Surface Area of Pyramids and Cones Check It Out! Example 2 Original Dimensions Triple the Slant HeightTriple the Radius S = r 2 + rl = (4.5) 2 + (4.5)(2) = 29.25in 2  91.8 in 2 S = r 2 + r(3l) = (4.5) 2 + (4.5)(6) = 47.25in 2  in 2 S = r) 2 + r)l = (13.5) 2 + (13.5)(2) = in 2  in 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 . They would not have the same effect. Tripling the radius would increase the surface area more than tripling the height.

Holt CA Course 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? = (10)(26)  mm 2 Pythagorean Theorem Lateral surface area L = rl a 2 + b 2 = l = l 2 l = 26

Holt CA Course 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? = (9)(15)  in 2 12 in. 9 in. Pythagorean Theorem a 2 + b 2 = l = l 2 l = 15 Lateral surface area L = rl

Holt CA Course 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 . 1. the triangular pyramid 2. the cone in m 2

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