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.

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


11