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

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

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

Surface Area of a Cone

S = B + (1/2) Cl S = πr 2 + (1/2)*(2πr)l S = πr 2 + πrl

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

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

Homework Pg –3,6,7,10,13,15,21-25