Question

A well of diameter 6m is dug 22m deep. The soil taken out of it is spread evenly all around it to a width of 5m to form an embankment. Find the height of the embankment.

Answer 1

Solution:-

A well is in the form of Cylinder.

=> Volume of Cylinder = Volume of soil dig out.

=> Volume of Cylinder

$= > \pi \: {r}^{2} h \\ \\ = > \frac{22}{7} \times 3 \times 3 \times 22$

=> Volume of Soil dig out = 622.28 cm^3.

Now,

Volume of Embankment

$= > \pi( {r1}^{2} - {r2}^{2} ) \times \: h \\ \\ = > \frac{22}{7} ( {5.5}^{2} - {3}^{2} ) \times h \\ \\ = > \frac{22}{7} \times (30.25 - 9) \times h \\ \\ = > \frac{22}{7} \times 21.25 \times h$
The Volume of soil is taken out and spread to form the embankment.

=> Volume of Embankment = Volume of Cylinder

$= > \frac{22}{7} \times 21.25 \times h = \frac{22}{7} \times 9 \times 22 \\ \\ = > 21.25 \times h = 22 \times 9 \\ \\ = > h = \frac{22 \times 9}{21.25} \\ \\ = > h = 9.31m$

Hence,

Height of Embankment is 9.31 m.