Question

A cylindrical shaped well of depth $20m$ and diameter $14m$ is dug. The dug out soil is evenly spread to form a cuboid-platform with base dimensions $20m\times 14m$. Find the height of the platform.

Answer 1

We have,

$depth\left(h\right)=20m$

$d=14m$

$\Rightarrow 2r=14m$

$\Rightarrow r=7m$

Volume of the cylinder $=\pi r^{2}h$

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

$=22\times 7\times 20m^3$

Since,

The length of cuboid $l=20m$

The breadth of cuboid $b=14m$

Let the height of cuboid be ${}^{\prime }{x}^{\prime }$.

So, the volume of the cuboid

$=l\times b\times h$

$=20\times 14\times x{m}^3$

According to the question,

$20\times 14\times x=22\times 7\times 20$

$2\times x=22$

$x=11m$

Hence, this is the answer.