# Solve this

Question:

Note Use $\pi=\frac{22}{7}$, unless stated otherwise.

A man uses a piece of canvas having an area of 551 m2, to make a conical tent of base radius 7 m. Assuming that all the stitching margins and wastage incurred while cutting, amount to approximately 1 m2, find the volume of the tent that can be made with it.

Solution:

Area of the canvas = 551 m2

Area of the canvas used in stitching margins and wastage incurred while cutting = 1 m2

∴ Area of the canvas used in making the tent = 551 − 1 = 550 m2

Radius of the tent, r = 7 m

Let the slant height and height of the tent be l m and h m, respectively.

Area of the canvas used in making the tent = 550 m2

$\therefore \pi r l=550$

$\Rightarrow \frac{22}{7} \times 7 \times l=550$

$\Rightarrow l=\frac{550}{22}=25 \mathrm{~m}$

Now,

Height of the tent, $h=\sqrt{l^{2}-r^{2}}=\sqrt{25^{2}-7^{2}}=\sqrt{625-49}=\sqrt{576}=24 \mathrm{~m}$

$\therefore$ Volume of the tent $=\frac{1}{3} \pi r^{2} h=\frac{1}{3} \times \frac{22}{7} \times(7)^{2} \times 24=1232 \mathrm{~m}^{3}$

Thus, the volume of the tent that can be made with the given canvas is 1232 m3.