Question

Note Use $\mathrm{\pi }=\frac{22}{7}$, 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.

Answer 1

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

$$\begin{gathered} \therefore \mathrm{\pi }rl=550 \\ \Rightarrow \frac{22}{7}\times 7\times l=550 \\ \Rightarrow l=\frac{550}{22}=25\mathrm{m} \end{gathered}$$

Now,

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

∴ Volume of the tent = $\frac{1}{3}\mathrm{\pi }{r}^{2}h=\frac{1}{3}\times \frac{22}{7}\times {\left(7\right)}^2\times 24$ = 1232 m³

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