Question 975487
Refer to your textbook or to this wikipedia article: https://en.wikipedia.org/wiki/Frustum .


If s is slant height, h is the frustrum height, and R and r are the bigger and smaller radii, then  you can form a right triangle from the frustrum with the Pythagorean Theorem equation  {{{s^2=(R-r)^2+h^2}}}
and
Surface Area of the frustrum is {{{pi(R-r)*s}}}.


The problem description gives you enough information for R and r, and you can find s.


{{{s=sqrt((R-r)^2+h^2)}}}
Surface Area is then {{{highlight_green(pi(R-r)*sqrt((R-r)^2+h^2))}}}.
Radii are each half of the given diameters.


{{{highlight(SurfacArea=pi(10+5)sqrt((10-5)^2+12^2))}}};
Compute the expression.