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Monica has a piece of Canvas whose area is $551 \mathrm{~m}^{2}$. She uses it to have a conical tent made, with a base radius of $7 \mathrm{~m}$. Assuming that all the stitching margins and wastage incurred while cutting amounts to approximately $1 \mathrm{~m}^{2}$. Find the volume of the tent that can be made with it.
It is given that:
Area of the canvas $=551 \mathrm{~m}^{2}$
Area that is wasted $=1 \mathrm{~m}^{2}$
Radius of tent = 7m, Volume of tent (v) = ?
Therefore the Area of available for making the tent $=(551-1)=550 \mathrm{~m}^{2}$
Surface area of tent $=550 \mathrm{~m}^{2}$
$\Rightarrow \pi r l=550$
⟹ l = 550/22 = 25 m
Slant height (l) = 25 m
We know that,
$1^{2}=r^{2}+h^{2}$
$25^{2}=7^{2}+h^{2}$
$\Rightarrow 625-49=h^{2}$
$\Rightarrow 576=h^{2}$
h = 24 m
Height of the tent is 24 m.
Now, volume of cone $=1 / 3 \pi r^{2} h$
$=1 / 3 * 3.14 * 7^{2} * 24=1232 \mathrm{~m}^{3}$
Therefore the volume of the conical tent is $1232 \mathrm{~m}^{3}$.
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