Question

If a solid cone of base radius r and height h is placed over a solid cylinder having same base radius and height as that of the cone, then the curved surface area of the solid so formed is __________.

Answer 1

Slant height of the cone, l = $\sqrt{r^2+h^2}$

Curved surface area of the solid

= Curved surface area of cone + Curved surface area of cylinder

$$\begin{gathered} =\mathrm{\pi }rl+2\mathrm{\pi }rh \\ =\mathrm{\pi }r\left(l+2h\right) \\ =\mathrm{\pi }r\left(\sqrt{r^2+h^2}+2h\right) \end{gathered}$$

If a solid cone of base radius r and height h is placed over a solid cylinder having same base radius and height as that of the cone, then the curved surface area of the solid so formed is $\underline{\mathrm{\pi }r\left(\sqrt{r^2+h^2}+2h\right)}$.