Question

a well of 2 metre diameter is dug 7m deep. the earth dug out is spread evenly all around it to a width
of 5 m to form an embankment. find the height of the embankment so formed

Answer 1

Let us assume shape of well is like a solid circular cylinder

Radius of cylinder, r = 2/2 = 1m

Depth(height) of well, h = 14m

Volume of right circular cylinder, V’ = π r2 h

---------(I)

Given that, length of embankment, l = 40 cm

Let width of the embankment be x m

Volume of the embankment, V’’ = π r2 h

= π ((1+x)2 – 1)2 x 0.4 -----------(II)

Since well is spread evenly to form the embankment, so their volumes, V’ = V’’

⇒ π × 14 = π ((1+x)2 – 1)2 x 0.4

⇒ x = 5m

∴ Height of the embankment, x = 5cm