Question

A closed hollow cone 24 cm high having base radius 7 cm is to be made using metal sheets. Find the capacity of the cone and the amount of sheet required to make the cone.

• A. $704c{m}^2$ and $1232c{m}^3$ respectively
• B. $1232c{m}^2$ and $704c{m}^3$ respectively
• C. $804c{m}^2$ and $1532c{m}^3$ respectively
• D. $514c{m}^2$ and $1032c{m}^3$ respectively

Answer 1

The correct option is A

$704c{m}^2$ and $1232c{m}^3$ respectively

$\begin{array}{cc}Given& h=24cm,r=7cm\\ \therefore & l=\sqrt{r^2+h^2}=\sqrt{7^2+{24}^2}\\ & =\sqrt{49+576}=\sqrt{625}=25cm\\ \therefore & Areaofsheetrequired=\pi r^2+\pi rl\\ & =\pi r(r+l)=\frac{22}{7}\times 7\times (7+25)\\ & =22\times 32=704c{m}^2\\ \therefore & Volumeofcone=\frac{1}{3}\pi r^{2}h\\ & =\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 24=1232c{m}^3\end{array}$