Question

Ram’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 measure of 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.

Answer 1

Solution:-

Dimensions of cylindrical tank are —

• Radius (r ₁) = 60 cm = 0.60 m

• Height (h ₁) = 95 cm = 0.95 m

∴ Volume of Tank = πr ² h

= 3.14 × 0.6 × 0.6 × 0.95

V 1 = 1.074 m³

The dimensions of cuboid shape sump are —

• Length (l) = 1.57 m

• Breadth (b) = 1.44 m

• Height (h) = 0.95 m

∴ Volume of the sump = l.b.h.

= 1.57 × 1.44 × 0.95 m³

V 2 = 2.148 m³

When the tank is completely filled from the sump, remained volume of the sump = V2 – V1

= 2.148 – 1.074

= 1.074 m³

Now the length and breadth will remain same for the sump but height of water level will decrease due to decrease in water level.

∴ Volume of the water in the sump = l × b × h ₂

⇒ 1.978 = 1.57 × 1.44 × h ₂

h ₂= 0.475m

Hence, the height of water, left in the tank = 0.475 m.

and the Volumes of tank and sump are,

V ₁ = 1.074 m³ & V ₂ = 2.148 m³ respectively

v₁/v₂₌1.074/2.148 = $\frac{1}{2}$