Q. 11

A well of diameter 2 m is dug 14 m deep. The earth taken out of it is spread evenly all around it to form and embankment of height 40 cm. Find the width of the embankment.

Answer :

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


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

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