Surface Area of Pyramids and Cones
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1 Practice A Find the surface area of each pyramid _ _ _ _ Find the surface area of each cone. Use 3.14 for _ _
2 Practice B Find the surface area of each pyramid _ _ _ _ Find the surface area of each cone. Use 3.14 for _ _
3 Practice C Find the surface area of each pyramid _ _ _ _ Find the surface area of each cone. Use 3.14 for _ _
4 Review for Mastery Finding the surface area of a pyramid or a cone involves knowing certain terms. These include: The base area: The base side: The radius: The slant height: Use the drawings to answer the questions. 1. How long is the base side of Figure B? 3. The perimeter of a pyramid s base is the length of its base side times the number of sides. What is the perimeter of Figure A? Of Figure B? 2. Which two figures have the same slant height? _ 4. The area of a cone s circular base is times its radius times itself. If is 3.14, what is the area of Figure C s base? _
5 Challenge Finding the Slant Height of a Cone Below are the top and side views of the same cone: Notice that the vertex is perfectly centered over the base. The dotted line in the side view shows that if the vertex were extended downward, it would form a line perpendicular to the base and passing through its center. This line is the altitude of the cone, and it is used in determining the slant height. Here is the formula: where r is the radius and H is the altitude. r 2 H 2, The formula for the surface area of a cone excluding its base is, thus, r r 2 H 2. For Exercises 1 5, use What is the slant height of a cone whose base radius is 5 cm and whose altitude is 12 cm? 3. How can you derive the formula for the surface area of a cone excluding its base (S B )? 2. What is the slant height of a cone whose base radius is 4 cm and whose altitude is 3 cm? _ 4. What is an application that might call for determining the surface of a cone but not the base? _ 5. What is the relationship between finding the slant height of a cone and the Pythagorean Theorem?
6 Problem Solving Solve the problems. 1. A three-sided pyramid and square pyramid both have a base perimeter of 30 cm and the same slant height and surface area. What is the base height of the three-sided pyramid? 3. The Ladrones Tower in Marbella, Spain, is a cone-shaped building with a base circumference of 12 m and a slant height of 14.7 m. Find the surface area of the structure. Hint: The formula C expresses the d relationship between the circumference and diameter of a circle. 2. The surface area of a cone is exactly 4,396 units 2. The radius of the circular base is 2 the slant height of 5 the cone. Find r and. Use 3.14 for. 4. The Transamerica Building in San Francisco is a square pyramid with a metal top. The metal top has a base perimeter of 43 m and a slant height of 65 m. How many square meters of aluminum were required for the top of the Transamerica Building? _ At the right is a square pyramid designed by Chinese-American architect I.M. Pei. Use it to answer the questions. Circle the letter of the correct answer. 5. The pyramid s base area is A 35 m B 140 m 2 C 1,225 m 2 D 122 m 6. The surface area is of the glass walls is A 1,890 m 2 B 2,112 m 2 C 4,114 m 2 D 6,028 m 2
7 Reading Strategies Formula for the surface area of a pyramid or cone S B L Surface Base Area Lateral Area Area base side (b) 2 1 slant height ( ) base perimeter (P) b base height (h) 1 slant height ( ) base perimeter (P) 2 (3.14) radius (r) 2 (3.14) radius (r) slant height ( ) 1. For the figure shown, what is: (a) the length of b? (b) the length of? (c) the surface area? 2. For the figure shown, what is: (a) the length of b? (b) the length of h? (c) the length of? (d) the surface area? 3. For the figure shown, what is: (a) the length of r? (b) the length of? (c) the surface area?
8 Puzzles, Twisters & Teasers Seeing Is Believing Some of the shapes below are nets that fold to form pyramids. Others do not. Trace each shape, then cut out and fold along the dotted lines. For each net that forms a pyramid, determine the surface area _ _ 7. _ Original content Copyright by EduPro, Inc. SR
9 LESSON 10-5 Practice A in yd cm ft ft in yd m m cm ft yd 2 Practice B cm ft ft in yd m m cm ft yd in cm 2 Practice C cm ft ft in yd in m cm ft ,318.8 m in m 2 Review for Mastery 1. 5 m 2. Figures A and C 3. The perimeter of Figure A is 16 m. The perimeter of Figure B is 15 m m 2 Challenge cm 2. 5 cm 3. You can derive the formula by starting with the formula for the surface area of a cone. Since the surface area of a cone is r 2 r and since r 2 is the area of the circular base, then the area of the cone excluding the base is r. You can substitute for using the formula r 2 H 2. The formula for the surface area of a cone without its base is r r 2 H Possible answer: the amount of material needed to construct a tepee, which uses the ground as a base 5. They are essentially the same relationship. The altitude and the base of the cone form the legs of a right triangle whose hypotenuse is the slant height of the cone. Therefore, r 2 H 2 and a 2 b 2 c are equivalent. Problem Solving cm 2. r 20 and The surface area is about 99 m ,397.5 square meters 5. C 6. A Reading Strategies 1. (a) 4 ft (b) 7 ft (c) 72 ft 2 2. (a) 6 ft (b) 5.2 ft (c) 8 ft (d) 87.6 ft 2 3. (a) 4 ft (b) 9 ft (c) ft 2 Puzzles, Twisters & Teasers m 2 2. Not a pyramid in ft 2 5. Not a pyramid cm 2 7. Not a pyramid
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