Question

How many metres of cloth $5m$ wide will be required to make a conical tent, the radius of whose base is $7m$ and whose height is $24m$?

Answer 1

Step 1: Find the slant height of the conical tent.

Given,

Width of the cloth $=5m$

The radius of the conical tent $r=7m$

Height of the conical tent $h=24m$

The slant height of the conical tent $l=\sqrt{r^2+h^2}$

$\Rightarrow l=\sqrt{7^2+{24}^2}$

$\Rightarrow l=\sqrt{49+576}$

$\Rightarrow l=\sqrt{625}$

$\therefore l=25m$ $\left(\because {25}^2=625\right)$

Step 2: Find the area of the cloth used for the conical tent.

The curved surface area of a cone of radius $r$ and slant height $l$ $=\mathrm{\pi rl}$ $sq.units$

So, area of the cloth $=\mathrm{\pi rl}$

$=\frac{22}{7}\times 7\times 25$ $\left(\because \mathrm{\pi }=\frac{22}{7}\right)$

$=\frac{22}{7}\times 7\times 25$

$=22\times 25$

$=550m^2$

$\therefore$ Area of cloth $=550m^2$

Step 3: Find the length of the cloth used for the conical tent.

Length of the cloth $=\frac{\mathrm{Area}\mathrm{of}\mathrm{cloth}}{\mathrm{width}\mathrm{of}\mathrm{cloth}}$

$=\frac{550}{5}$

$=110m$

$\therefore$ Length of the cloth $=110m$.

Hence, length of the cloth is $110m$