Question

A well with inner radius 4 m is dug 14 m deep. Earth taken out of it has been spread evenly all around a width of 3 m it to form an embankment. Find the height of the embankment.

Answer 1

Let r and h be the radius and depth of the well respectively.

Given, r = 4 m and h = 14 m

Volume of earth dugged out of the wall$=\pi r^{2}h=\pi \times 4^2\times 14$m

Let R and H be the outer radius and height of the embankment.

∴ R = Radius of the well + Width if the embankment = 4 cm + 3 cm = 7 cm

Volume of the earth in the embankment $=\pi (R^2-r^2)H=\pi (7^2-4^2)H$

Now, Volume of the earth in the embankment = Volume of earth dugged out of the wall

$=>\pi (7^2-4^2)h=\pi \times 4^2\times 14$

$=>(49-16)h=16\times 14$

$=>h=\frac{224}{33}=6.79m$

Thus, the height of the embankment is approximately 6.79 m.