Question

A well is dug 21m deep. The earth taken out of it spread around it to form an embankment of height 4m and outer radius 5m. Find the radius of well

Answer 1

Given :

The height of the well = h = 21 meters

The height of the embankment = H = 4 meters

The outer radius of the embankment = R = 5 meters

To Find :

The radius of the well

Solution :

Let The radius of the well = r meters

∵ volume of well = volume of cylinder = π × radius² × height

                           = π × r² × h

                           = π × r² × 21 meters

Again

For embankment

Volume of embankment = volume of cylinder = π × ( 5 - r )² × 4

∵ Volume of embankment =  Volume of well

∴ π × ( 5 - r )² × 4 =  π × r² × 21

Or, ( 25 + r² - 10 r ) 4 = 21 r²

or,  100 + 4 r² - 40 r = 21 r²

Or, 17 r² + 40 r - 100 = 0

Solving this quadratic equation

   r = $\dfrac{- 40\pm \sqrt{(-40)^{2}-4\times 17\times (-100)}}{2 \times 17}$

     = 1.5 , - 3.8

So, radius = r = 1.5 m

Hence, The radius of well is 1.5 meters   . Answer