A Frustum of a Cone

The surface area of a frustum of a cone is equal to the area of the bases plus the lateral area. The lateral area is given by $A_L=\dfrac{1}{2}(c+C)(L)$ where $c$ and $C$ are the circumferences of the bases and $L$ is the slant height. So

$\text{surface area}= \pi (10^2)+ \pi (5^2) + \dfrac{1}{2}(20 \pi + 10 \pi)(13) = 125 \pi + 195 \pi = \boxed{320 \pi}$