Question

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

Answer 1

Let the height of the embankment be ‘h’ m 

Radius of well = \(\frac{3}2\) m

=1.5 m 

Height of the well =14 m 

Volume of earth dug out (volume of cylinder) = πr²h

= \(\frac{22}7\times{1.5}\times{1.5}\times{14}\) m³

= 99 m³ 

Outer Radius of the embankment(R) =1.5 m + 4 m 

= 5.5 m 

Inner radius of the embankment(r) =1.5 m 

Volume of embankment =Volume of earth dug out 

Volume of embankment = πR²h - πr²h

= πh(5.5² - 1.5²)

= 27.5πh 

Volume of embankment =Volume of earth dug out 

⇒ 27.5π h = 99 

⇒ h = \(\frac{{99}\times{7}}{{27.5}\times{22}}\) m

⇒ h = \(\frac{9}8\) = 1.125 m