Monica has a piece of Canvas whose area is 551m2.

Question:

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.

Solution:

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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