Question

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 × 1.44 m × 95cm. The overhead tank has its radius 60 cm and height 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)

Answer 1

The volume of water in the overhead tank equals the volume of the water removed from the sump.

Now, the volume of water in the overhead tank (cylinder) = $\pi r^{2}h$

= 3.14 × 0.6 × 0.6 × 0.95 $m^3$

The volume of water in the sump when full = l × b × h= 1.57 × 1.44 × 0.95 $m^3$

The volume of water left in the sump after filling the tank

= [(1.57 × 1.44 × 0.95) - (3.14 × 0.6 × 0.6 × 0.95)] $m^3$ = (1.57 × 0.6 × 0.6 × 0.95 × 2) $m^3$

So, the height of the water left in the sump = $\frac{volumeofwaterleftinthesump}{l\times b}$

= $\frac{1.57\times 0.6\times 0.6\times 0.95\times 2}{1.57\times 1.44}$m

= 0.475 m = 47.5 cm
Also,

$\frac{Capacityoftank}{Capacityofsump}=\frac{3.14\times 0.6\times 0.6\times 0.95}{1.57\times 1.44\times 0.95}=\frac{1}{2}$
Therefore, the capacity of the tank is half the capacity of the sump.