Selvi's house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (an underground tank) which is in the shape of a cuboid. The sump has dimensions $1.57 \, m \times 1.44 \, m \times 95 \, cm$. The overhead tank has a radius of $60 \, cm$ and a height of $95 \, cm$. Find the height of the water left in the sump after the overhead tank has been completely filled with water from the sump which had been full. Compare the capacity of the tank with that of the sump. (Use $\pi = 3.14$)

(D) The volume of water in the overhead tank equals the volume of water removed from the sump.
Volume of the overhead tank (cylinder) $= \pi r^2 h = 3.14 \times 0.6 \, m \times 0.6 \, m \times 0.95 \, m = 1.07388 \, m^3$.
Volume of the sump (cuboid) $= l \times b \times h = 1.57 \, m \times 1.44 \, m \times 0.95 \, m = 2.14776 \, m^3$.
Volume of water left in the sump $= 2.14776 \, m^3 - 1.07388 \, m^3 = 1.07388 \, m^3$.
Let the height of the water left in the sump be $H$. Since the base area of the sump remains constant,$l \times b \times H = 1.07388 \, m^3$.
$1.57 \, m \times 1.44 \, m \times H = 1.07388 \, m^3$.
$2.2608 \, m^2 \times H = 1.07388 \, m^3$.
$H = \frac{1.07388}{2.2608} \, m = 0.475 \, m = 47.5 \, cm$.
Ratio of capacities $= \frac{\text{Capacity of tank}}{\text{Capacity of sump}} = \frac{1.07388}{2.14776} = \frac{1}{2}$.
Thus,the capacity of the tank is half the capacity of the sump.