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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 $2.5 \mathrm{~m}$.