(Q4).Pravali house has a water tank in the shape of a cylinder on the roof. 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 × 9.5 cm. The water tank has radius 60 cm and height 95 cm. Find the height of the water left in the sump after the water tank has been completely filled with water from the sump which had been full of water. Compare the capacity of the tank with that of the sump, (π = 3.14)

Answer:

Volume of the water in the sump = × × [∵ V = lbh]

= m3 = cm3

Volume of the tank on the roof = πr2h

= × × ×

= cm3

∴ Volume of the water left in the sump after filling the tank

= – = cm3

Let the height of the water in the tank be h.

∴ × =

h =
×
 = cm.

∴ Ratio of the volume of the sump and tank = :

= :

∴ Sump can hold times the water that can be hold in the tank.