A solid cone of radius '$r$' and height '$h$' is placed on the top of a solid cylinder with the same base radius and height as a cone. Find the total surface area of the combined solid.

The combined solid is represented below.

TSA of the combined solid

$=$ CSA of cone + CSA of cylinder + Base area of the cylinder

$=\pi rl+2\pi rh+\pi r^2$

$=\pi r(l+2h+r)$

We know, $l=\sqrt{r^2+h^2}$

Therefore, TSA of the combined solid$=\pi r\left(\sqrt{r^2+h^2}+r+2h\right)$