A well of inner diameter 14 m is dug to a depth of 15 m. Earth taken out of it has been evenly spread all around it to a width of 7 m to form an embankment. Find the height of embankment so formed.

Let the height of embankment be h.

Volume of earth taken out = \( \Large \pi r^{2}h \)

= \( \Large \frac{22}{7} \times \left(7\right)^{2} \times 15 \)

Embankment >>!IMAGE!<<

Volume of earth taken out = Volume of embankment

[an embankment is a heap of stone or mud or earth to stop water]

\( \Large \pi r^{2}h = \pi \left(r_{1} + r_{2}\right)^{2}h - \pi r_{1}^{2}h \)

[Because \( \Large r_{1} = 7, r_{2} = 7 \)]

=> \( \Large \frac{22}{7} \times 7^{2} \times 15 = \frac{22}{7} \left(14^{2} - 7^{2}\right)h \)

Therefore, \( \Large h = \frac{7^{2} \times 15}{196 - 49} = 5 m \)