Question

A well of diameter 4 m is dug 21 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 3 m to form an embankment. Find the height of the embankment.

Answer 1

Answer:

The height  of the embankment is 3.36 m.                  

Step-by-step explanation:

Diameter of well = 4 m

Radius of well = $\frac{Diameter}{2} = \frac{4}{2} =2 m$

Depth of well = 21 m

Well is in the shape of cylinder

Volume of well = $\pi r^{2} h$

                         = $3.14 \times 2^{2} \times 21$

                         = $263.76 m^3$

Now we are given that The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 3 m to form an embankment.

So, radius of embankment = Radius of well + width

                                             = 2 + 3

                                             = 5 m

Embankment is in the shape of cylinder .

So, volume of embankment =  $\pi r^{2} h$

                                               = $3.14 \times 5^{2} \times h$

                                               = $78.5h$

Since the earth is taken out from the well is used to make embankment So, volume will be equal.

$\Rightarrow 263.76 =78.5h$

$\Rightarrow \frac{263.76}{78.5}=h$

$\Rightarrow 3.36=h$                        

Hence the height  of the embankment is 3.36 m.