Question

A solid cone of radius $r$ and height $h$ is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is

• A. $\pi r[\sqrt{r^2+h^2}+r+2h]$
• B. $\pi r[\sqrt{r^2+h^2}+2r+3h]$
• C. $\pi r[2\sqrt{r^2+h^2}+3r+2h]$
• D. none of these

Answer 1

The correct option is A $\pi r[\sqrt{r^2+h^2}+r+2h]$

The combined solid is represented in above fig.

TSA of new solid $=$ CSA of Cone $+$ CSA of cylinder $+$ Base area of cylinder

TSA of solid $=\pi rl+2\pi rh+\pi r^2$

TSA of solid $=\pi r(l+2h+r)$

TSA of solid $=\pi r(\sqrt{r^2+h^2}+2h+r)$