Question:
A well is dug 20 m deep and it has a diameter of 7 m. The earth which is so dug out is spread out on a rectangular plot 22 m long and 14 m broad. What is the height of the platform so formed?
Solution:
Height of the well = h m = 20 m
Diameter of the well = d m =7 m
Radius of the well = r m = 3.5 m
Volume of the well = πr2h = $\frac{22}{7}(3.5)^{2}(20) \mathrm{m}^{3}=770 \mathrm{~m}^{3}$
Volume of the well = Volume of the rectangular plot
Length of the rectangular plot = 22 m
Breadth of the rectangular plot =14 m
Volume of the rectangular plot = 770 m3 = (Length
Height $=\frac{770}{22 \times 14}=2.5 \mathrm{~m}$
Thus, the height of the platform is 2.5 m.