Question

A well is dug with 14 m diameter and a depth of 10 m. The earth taken out is spread evenly on a plot of land 100 m long and 7 m wide. Find the height of the platform thus formed be the earth.

Answer 1

Answer :–

The height of the platform formed = 2.2 m

______________________

Solution :—

The volume of earth dug out

= The volume of the well

Depth of the well = 10 m

Radius of the well = $\dfrac{14}{2}\:= \:7\: m$

.

The well is cylindrical in shape, hence the formula for the volume of a cylinder would be used to find the volume of the well.

.°. Volume of well = πr²h

.

$= \: \dfrac{22}{ \cancel 7 } \: \times \: \cancel 7 \: \times \: 7 \: \times \: 10 \: = \: 1540 \: m {}^{3}$

The platform formed is a cuboid in shape whose

length = 100 m , breadth = 7 m and height needs to found out.

.

Volume of the platform

= Volume of the earth dug out = 1540 m³

Substituting these values in the formula

V = l × b × h , we get

1540 = 100 × 7 × h

$h \: = \: \dfrac{1540}{100 \times 7} \: = \: 2.2 \: m$

.

.°. The height of the platform formed = 2.2 m