Question

A well of inner diameter 14 m is dug to a depth of 12 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 the embankment so formed.

Answer 1

Let height of embankment be ${}^{\prime }{h}^{\prime }$ meter. Then

Volume of embankment $=$ Volume of earth taken out from the well

$\Rightarrow \pi (R^2-r^2)h=\pi r^{2}H$

$\Rightarrow ({(7+7)}^2-7^2)\times h=7^2\times 12$

$\Rightarrow (196-49)\times h=49\times 12\Rightarrow h=\frac{49\times 12}{147}=4m$

$\therefore$ Height of embankment $=4m$.