A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m.

Question:

A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used, at the rate of 25 per metre.

Solution:

We have,

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

Radius of the conical tent, $r=\frac{14}{2}=7 \mathrm{~m}$ and

Height of the conical tent, $h=24 \mathrm{~m}$

Let the length of the cloth used for making the tent be $L$.

Also,

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

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

$=\sqrt{49+576}$

$=\sqrt{625}$

$=25 \mathrm{~m}$

Now,

The curved surface of the conical tent $=\pi r l$

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

$\Rightarrow$ The area of the cloth used for making the tent $=550 \mathrm{~m}^{2}$

$\Rightarrow L B=550$

$\Rightarrow L=\frac{550}{B}$

$\Rightarrow L=\frac{550}{5}$

$\Rightarrow L=110 \mathrm{~m}$

So, the cost of the cloth used $=25 \times 110=₹ 2750$

So, the cost of the cloth used for making the tent is ₹2750.