Question

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 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’ = πr² h 

= \(π\times{1}^2\times14\)---------(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 = 5 m 

∴ Height of the embankment, x = 5cm