Question

What is the surface area of the right cone below?

Answer 1

First find height using Pythagorean theorem.

$h^2+4^2=13^2\implies h=\sqrt{153}\approx12.37$.

Then use cone surface area formula and compute the result:

$A=\pi r(r+\sqrt{h^2+r^2})\approx\boxed{68\pi}\mathrm{units^2}$.

Hope this helps.