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Surface Area of Pyramids and Cones

Surface Area of Pyramids and Cones. 12.3. Surface Area of a Pyramid. S = Area of the Base * 6 *Area of each triangle S = B * 6(1/2(b*l)) S = B*(1/2)(6b)(l) where 6b equal the perimeter S = B * (1/2)Pl. Find the surface area of the regular hexagonal pyramid. 1. 1.

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Surface Area of Pyramids and Cones

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  1. Surface Area of Pyramidsand Cones 12.3

  2. Surface Area of a Pyramid

  3. S = Area of the Base * 6 *Area of each triangle • S = B * 6(1/2(b*l)) • S = B*(1/2)(6b)(l) where 6b equal the perimeter • S = B * (1/2)Pl

  4. Find the surface area of the regular hexagonal pyramid. 1 1 First, find the area of the base using the formula for the area of a regular polygon, aP. The apothem aof the hexagon is 5√ 3 feet and the perimeter Pis 6 10= 60feet. So, the area of the base Bis (5√ 3)(60) = 150√ 3 square feet. Then, find the surface area. 2 2 Find the surface area of a pyramid EXAMPLE 2 SOLUTION

  5. S = B + Pl = 150√ 3 + (60)(14) 1 1 2 2 = 150√ 3 + 420 ANSWER The surface area of the regular hexagonal pyramid is about 679.81 ft2. Find the surface area of a pyramid EXAMPLE 2 Formula for surface area of regular pyramid. Substitute known values. Simplify. ≈ 679.81 Use a calculator.

  6. Surface Area of a Cone

  7. S = B + (1/2) Cl • S = πr2 + (1/2)*(2πr)l • S = πr2 + πrl

  8. The traffic cone can be approximated by a right cone with radius 5.7 inches and height 18inches. Find the approximate lateral area of the traffic cone. Find the lateral area of a cone EXAMPLE 4 TRAFFIC CONE SOLUTION To find the slant height l,use the Pythagorean Theorem. l2 = 182 + (5.7)2, sol≈ 18.9 inches.

  9. ANSWER The lateral area of the traffic cone is about 338.4 square inches. Find the lateral area of a cone EXAMPLE 4 Find the lateral area. Lateral area = πrl Write formula. = π(5.7)(18.9) Substitute known values. ≈ 338.4 Simplify and use a calculator.

  10. Homework • Pg 814-815 • 3,6,7,10,13,15,21-25

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