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# A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.

Given:

A 20 m deep well with a diameter of 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m.

To do:

We have to find the height of the platform.

Solution:

Diameter of the well $=7 \mathrm{~m}$

This implies,

Radius of the well $r=\frac{7}{2} \mathrm{~m}$

Depth of the well $h=20 \mathrm{~m}$

Therefore,

The volume of the earth dug up $=\pi r^{2} h$

$=\frac{22}{7} \times(\frac{7}{2})^{2} \times 20$

$=\frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 20$

$=770 \mathrm{~m}^{3}$ Length of the platform $l=22 \mathrm{~m}$

Breadth of the platform $b=14 \mathrm{~m}$

Let $h$ be the height of the platform.

The volume of the platform $=l b h$

$=22 \times 14 \times h$

The volume of the earth dug up $=$ Volume of the platform

$\Rightarrow 22 \times 14 \times h=770$

$\Rightarrow h=\frac{10}{4}$

$\Rightarrow h=\frac{5}{2}$

$\Rightarrow h=2.5 \mathrm{~m}$

The height of the platform is $2.5 \mathrm{~m}$.

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