jmc

Question

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

π

.

Accepted Answer

The circumferences of the bases are 2 4 = 8 and 2 10 = 20 . To find the slant height, we drop perpendiculars. FIGURE We have created a right triangle with legs 6 and 8, so the hypotenuse is L = 10. Hence, the total surface area of the frustum, including the two bases, is 4^2 + 10^2 + 12 10 (8 + 20 ) = 256 .