Question

A $5m$ wide cloth is used to make a conical tent of base diameter $14m$ and height $24m$. Find the cost of cloth used at the rate of Rs. $25$ per metre (Use $\pi =22/7$)

Answer 1

Let the slant height of the cone be 'l' meters.

height $=24$ m and diameter $=14$ m or radius $=7$ m.

Then according to the question.

$l²=h²+r²$

$l^2={24}^2+7^2$

$l^2=576+49$

$l^2=625$

$l=\sqrt{625}m$

$l=25$ m

So, the slant height of the cone is $25$ m.

Now,

Curved Surface Area of the cone $=\pi rl$= $\frac{22}{7}\times 7\times 25$

$CSA=550m^2$

Now, length of the cloth used = Area/ width of the cloth$= \dfrac{550}{5}$

Length of the cloth used $=110m$

Cost of cloth $=Rs.25/meter$

Total cost of clothe used $25\times 110=Rs.2750$