Question

The base radius and height of a cube are $7cm$ and $24cm$ respectively. Find it slant height, lateral surface area, total surface area and volume.

Answer 1

Given, The base radius of cone $=7cm$ Height $\left(h\right)=24cm$
$\therefore$ Slant height $=\sqrt{r^2+h^2}$
$\begin{array}{c}=\sqrt{(7{)}^2+(24{)}^2}\\ =\sqrt{49+576}\\ =\sqrt{625}\\ =25cm\end{array}$
Curved surface area of cone $=\pi rl$
$\begin{array}{c}=\frac{22}{7}\times 7\times 25\\ =22\times 25\\ =550{cm}^2\end{array}$
Total surface area of cone $=\pi r(l+r)$
$\begin{array}{c}=\frac{22}{7}\times 7(25+7)\\ =22\times 32\\ =704{cm}^2\end{array}$
Volume of the cone $=\frac{1}{3}\pi r^{2}h$
$\begin{array}{c}=\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 24\\ =\frac{3696}{3}=1232{cm}^3\end{array}$
Hence slant height of cone 25 cm, curved surface area=$550c{m}^2$, total surface area=$704c{m}^2$ and volume=$1232c{m}^2$