Question

A well with inside diameter $10m$ is dug $8.4m$ deep. Earth taken out of it is spread all around it to width of $7.5m$ to form an embankment. Find the height of the embankment.

Answer 1

Since, inner diameter is $10m$, therefore,

Inner radius $r=\frac{10}{2}=5m$

Height of the well $=8.4m$

Therefore, volume of the well $=\pi r^{2}h$

$=\frac{22}{7}\times 5\times 5\times 8.4$

$=660m^3$

According to the question,

Volume of well $=$ Volume of earth taken out

Now, radius of outer cylinder/well $R=5+7.5=12.5m$

Area of the embankment $=\pi (R^2-r^2)$

$=\frac{22}{7}\times (156.25-25)$

$=412.5m^2$

Now, height of the embankment $=$ Volume of earth earth dug out $÷$ Area of embankment

Therefore, Required height $=\frac{660}{412.5}=1.6m$