Question

Selvi's house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (underground tank). Which is in the shape of a cuboid. The sump has dimensions $1.57m\times 1.44m\times 0.95m$. The overhead tank has its radius of $60cm$ and its height is $95cm$. Find the height of the water, left in the sump after the overhead tank has been completely filled with water from a sump which had been full. Compare the capacity of the tank with that of the sump (Use $\pi =22/7$)

Answer 1

Clearly the volume of the water in the overhead tank is equal to the volume of the water removed from the sump.

Now Volume of water in the overhead tank $=3.14\times 0.6\times 0.6\times 0.95m^3=3.14\times 0.36\times 0.95m^3$

Volume of water in the sump when it is full of water $=1.57\times 1.44\times 0.95m^3=1.57\times 4\times 0.36\times 0.95m^3=2\times 3.14\times 0.36\times 0.95m^3$

Volume of water left in the sump after filling the tank

$(2\times 3.14\times 0.36\times 0.95-3.15\times 0.36\times 0.95)m^3=3.14\times 0.36\times 0.95m^3$

Area of the base of the sump $=1.57\times 1.44m^3=1.57\times 4\times 0.36m^3=2\times 3.14\times 0.36m^3$

Height of the water in the sump $=\frac{3.14\times 0.36\times 0.95}{2\times 3.14\times 0.36}m=\frac{0.95}{2}=47.5cm$

Now $\frac{capacityoftank}{capacityofsump}=\frac{3.14\times 0.36\times 0.95}{2\times 3.14\times 0.36\times 0.95}=\frac{1}{2}$