Question

A 10 m deep well of diameter 1.4 m is dug up in a field and the earth from digging is spread evenly on the adjoining cuboid field. The length and breadth of that field are 55m and 14m respectively. Find the thickness of the earth layer spread.

Answer 1

Radius of the well = $\frac{\mathrm{Diameter}}{2}=\frac{1.4}{2}=0.7\mathrm{m}$

Depth of the well = 10 m
Volume of the earth dug out = $\mathrm{\pi }$r²h
= $\frac{22}{7}$× (0.7)² × 10
= 15.4 m³
Now,
Length of the cuboid = 55 m
Breadth of the cuboid = 14 m

Volume of the cuboid = Volume of the earth dug out

$$\begin{gathered} \Rightarrow lbh=15.4 \\ \Rightarrow 55\times 14\times h=15.4 \\ \Rightarrow h=\frac{15.4}{55\times 14} \\ \Rightarrow h=0.02\mathrm{m} \end{gathered}$$

Hence, the thickness of the earth is 0.02 m.