A $ 16 \mathrm{~m} $ deep well with diameter $ 3.5 \mathrm{~m} $ is dug up and the earth from it is spread evenly to form a platform $ 27.5 \mathrm{~m} $ by $ 7 \mathrm{~m} $. Find the height of the platform.

Given:

A \( 16 \mathrm{~m} \) deep well with diameter \( 3.5 \mathrm{~m} \) is dug up and the earth from it is spread evenly to form a platform \( 27.5 \mathrm{~m} \) by \( 7 \mathrm{~m} \).

To do:

We have to find the height of the platform.

Solution:

Diameter of the well $=3.5 \mathrm{~m}$

This implies,

Radius of the well $r=\frac{3.5}{2}$

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

$=\frac{7}{4} \mathrm{~m}$

Depth of the well $h=16 \mathrm{~m}$

Therefore,

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

$=\frac{22}{7} \times(\frac{7}{4})^{2} \times 16$

$=\frac{22}{7} \times \frac{7}{4} \times \frac{7}{4} \times 16$

$=154 \mathrm{~m}^{3}$
Length of the platform $l=27.5 \mathrm{~m}$

Breadth of the platform $b=7 \mathrm{~m}$

Let $h$ be the height of the platform.

Volume of the platform $=l b h$

$=27.5 \times 7 \times h$

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

$\Rightarrow 27.5 \times 7 \times h=154$

$\Rightarrow h=\frac{154}{7 \times 27.5}$

$\Rightarrow h=\frac{154 \times 10}{7 \times 275}$

$\Rightarrow h=0.8 \mathrm{~m}$

$\Rightarrow h=0.8\times100=80 \mathrm{~cm}$

The height of the platform is $80 \mathrm{~cm}$.

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Updated on: 10-Oct-2022

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