Question

A well $20m$ in diameter is dug $14m$ deep and the earth taken out is spread all round it to a width of $5m$ to form an embankment. The height of the embankment is

• A. $10m$
• B. $11m$
• C. $11.2m$
• D. $11.5m$

Answer 1

The correct option is C $11.2m$

The well dug is in the shape of a cylinder.

Radius of the well $=\frac{20}{2}=10m$

Volume of a Cylinder $=\pi R^{2}h$
Hence, Volume of earth taken out from the well $=\pi \times 10\times 10\times 14=1400\pi m^3$

The embankment would form a circular ring with internal radius same as radius of the well $=10m$

And external radius $=10+5=15m$
Area of embankment $=\pi \times ({15}^2-{10}^2)=\pi \times \left(1510\right)\times (15+10)=125\pi$
Height of the embankment $=\frac{Volume}{Area}=\frac{1400\pi }{125\pi }=11.2m$