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# The lateral surface area of the frustum of a solid right cone is the product of one-half the slant height ($L$) and the sum of the circumfer

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The lateral surface area of the frustum of a solid right cone is the product of one-half the slant height ($L$) and the sum of the circumferences of the two circular faces. What is the number of square centimeters in the total surface area of the frustum shown here? Express your answer in terms of $\pi$.

michaelcai  Oct 24, 2017
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Area of the "side"  =

pi * (  sum of the top and bottom radii) * sqrt [ ( diffrence of radii)^2 + height^2 ] =

pi * ( 10 +  4 ) * sqrt [ (10 - 4)^2 + 8^2 ]  =

pi * (14) * sqrt [ 100]  =

pi * 14 * 10  =

140 pi  cm^2

Area of top/bottom  =  pi  [ 10^2 + 4^2]  =   116 pi cm^2

So....the total surface area is    [ 140 + 116] pi cm^2  =   256 pi cm^2

CPhill  Oct 24, 2017

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