Monica has a piece of Canvas whose area is $$551$$ $$m^2$$. She uses it to have a conical tent made, with a base radius of $$7$$m. Assuming that all the stitching margins and wastage incurred while cutting, amounts to approximately $$1$$ $$m^2$$. Find the volume of the tent that can be made with it. $$($$in $$m^3)$$
Correct option is A. 1232
We have,
Area of canvas$$=551m^2$$
and Area of canvas lost in wastage$$=1m^2$$.
$$\therefore$$ Area of canvas used in making tent$$=(551-1)m^2=550m^2$$.
$$\Rightarrow$$ Surface area of the cone$$=550m^2$$.
We have,
$$r=$$radius of the base of the cone$$=7$$m.
$$\therefore$$ surface area$$=550m^2$$
$$\Rightarrow \pi rl=550$$
$$\Rightarrow \dfrac{22}{7}\times 7\times l=550$$
$$\Rightarrow l=25$$m.
Let $$h$$ be the height of the cone. Then,
$$l^2=r^2+h^2\Rightarrow h=\sqrt{l^2-r^2}=\sqrt{25^2-7^2}=24$$m.
$$\therefore$$ Volume of the cone$$=\dfrac{1}{3}\pi r^2h=\dfrac{1}{3}\times \dfrac{22}{7}\times 7\times 7\times 24m^3=1232m^3$$.