Question

if a right circular cone of vertical height h 20cm has a volume of 1232 cubic cm, find the CSA

Answer 1

Dear Student,

Volume is given, we can calculate the radius from it, then by calculating slant height, we can get curved surface area,

$$\begin{gathered} V=\frac{1}{3}\pi r^{2}h \\ 1232=\frac{1}{3}\pi r^{2}20 \\ {r}^2=\frac{1232\times 3}{20\times 3.14}=58.85 \\ r=7.67cm. \\ L=\sqrt{r^2+h^2}\hspace{0.17em}(l-slantheight). \\ L=\sqrt{7.{67}^2+{20}^2}=21.42cm. \\ Curvedsurfacearea=\pi rL=3.14\times 7.67\times 21.42=516.13c{m}^2 \end{gathered}$$
Regards.