A $ 5 \mathrm{~m} $ wide cloth is used to make a conical tent of base diameter $ 14 \mathrm{~m} $ and height $ 24 \mathrm{~m} $. Find the cost of cloth used at the rate of $ ₹ 25 $ per metre. [Use $ \pi=22 / 7] $

Given:

A \( 5 \mathrm{~m} \) wide cloth is used to make a conical tent of base diameter \( 14 \mathrm{~m} \) and height \( 24 \mathrm{~m} \).

To do:

We have to find the cost of cloth used at the rate of \( ₹ 25 \) per metre.

Solution:

Diameter of the base of the conical tent $= 14\ m$

This implies,

Radius of the base $r= \frac{14}{2}$

$=7\ m$

Height of the cone $h = 24\ m$

This implies,

Slant height of the cone $l=\sqrt{r^{2}+h^{2}}$

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

$=\sqrt{49+576}$

$=\sqrt{625}$

$=25 \mathrm{~m}$

Therefore,

Curved surface area of the cone $=\pi r l$

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

$=550 \mathrm{~m}^{2}$

Width of the cloth used $=5 \mathrm{~m}$

This implies,

Length of the cloth used $=\frac{Curved\ surface\ area}{width}$

$=\frac{550}{5}$

$=110 \mathrm{~m}$

Rate of cloth per $m^2=Rs.\ 25$

Total cost of cloth used $=Rs.\ 110 \times 25$

$=Rs.\ 2750$

The cost of cloth used is $Rs.\ 2750$.