Question

The height and radius of the base of a cone are $28cm$ and $21cm$ respectively. Find its curved surface area, total surface area, and the volume.

Answer 1

Given, height of cone $\left(h\right)=28cm$.
Radius of base $\left(r\right)=21cm$
Slant height of the cone $l=\sqrt{r^2+h^2}$
$\begin{array}{cc}& =\sqrt{(21{)}^2+(28{)}^2}\\ & =\sqrt{441+784}\\ & =\sqrt{1225}\\ & =\sqrt{35\times 35}\\ & =35cm\\ \text{Curved surface area}& =\pi rl\\ & =\frac{22}{7}\times 21\times 35\\ & =2310{cm}^2\end{array}$
Total surface area of the cone
$\begin{array}{c}=\pi r(l+r)\\ =\frac{22}{7}\times 21(35+21)\\ =22\times 3\times 56\\ =3696{cm}^2\end{array}$
Volume of the cone $=\frac{1}{3}\pi r^{2}h$
$=\frac{1}{3}\times \frac{22}{7}\times 21\times 21\times 28$
$=12936{cm}^3$