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.

 Given:

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 $7\ m$. 

The stitching margins and wastage incurred while cutting, amounts to approximately $1\ m^2$.

To do:

We have to find the volume of the tent that can be made with it.

Solution:

Area of the canvas $= 551\ m^2$

Area of wastage $= 1\ m^2$

This implies,

Actual area $= 551 - 1$

$= 550\ m^2$

Base radius of the conical tent $= 7\ m$

Let $l$ be the slant height and $h$ be the vertical

height of the cone.

Therefore,

Slant height of the cone $(l)=\frac{\text { Area }}{\pi r}$

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

$=25 \mathrm{~m}$

Vertical height of the cone $(h)=\sqrt{l^{2}-r^{2}}$

$=\sqrt{25^{2}-7^{2}}$

$=\sqrt{625-49}$

$=\sqrt{576}$

$=24 \mathrm{~m}$

Volume of the tent $=\frac{1}{3} \pi r^{2} h$

$=\frac{1}{3} \times \frac{22}{7} \times 7 \times 7 \times 24$

$=1232 \mathrm{~m}^{3}$

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Updated on: 10-Oct-2022

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