12.3 Surface Area of Pyramids and Cones

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Presentation transcript:

12.3 Surface Area of Pyramids and Cones Hubarth Geometry

Vertex Height Slant height Base

Ex 1 Find the Slant Height Find the slant height of the Rainforest Pyramid. Round your answer to the nearest whole number. 100ft 200ft Solution 200ft

Theorem 12.4 Surface Area of a Pyramid

Ex 2 Find the Surface Area of a Pyramid Find the surface area of the pyramid. 4ft Solution 6ft 6ft 1. Find the area of the base. B= (6)(6)=36 2. Find the perimeter of the base. P= 6+6+6+6= 24

Ex 3 Find the Surface Area of a Pyramid Find the surface area of the regular hexagonal pyramid. First, find the area of the base. Find the area of one triangle inside the Hexagon and then times by the number of sides. (10)(5 3 ) 2 =43.3 B= 43.3(6)=259.8 S = B + 1 2 Pl = 259.8 + 1 2 (60)(14) = 259.8 + 420 ≈ 679.8

Theorem 12.5 Surface Area of a Cone l r

Ex 3 Find the Surface Area of a Cone Find the surface area of the cone to the nearest whole number. a. b. 4in 5ft 6in 12ft Solution

Ex 4 Standardized Test Practice To find the slant height l of the right cone, use the Pythagorean Theorem. l2 = h2+ r 2 l2 = 82 + 62 l = 10 Use the formula for the surface area of a right cone. S = πr2 + πrl = π(62) + π(6)(10) = 96π The correct answer is B.

Find the surface area of the pyramid. Practice Find the surface area of the pyramid. 1. 2. 12ft 10ft 12 10ft 3. Find the surface area of the cone to the nearest whole number 3cm 4cm