Question

The diameter of the cross-section of a water pipe is 5 cm. Water flows through it at 10km/hr into a cistern in the form of a cylinder. If the radius of the base of the cistern is 2.5 m, find the height to which the water will rise in the cistern in 24 minutes.

Answer 1

Area of the cross-section of the water pipe = πr²
= 3.142 x `5/2 xx 5/2`

Speed of the water = 10 km/hr 
= `(10 xx 1000 xx 100)/60` cm/minutes

∴ Quantity of water supplied in 24 minutes
= `3.142 xx 5/2 xx 5/2 xx (10,00,000)/6 xx 24`

= 78,55,000 cm³

Let the height of water in the cistern be h cm.
The quantity of water collected in the cistern
= 3.142 x 250 x 250 x h cm³

Both the above quantities must be equal 

∴ 3.142 x 250 x 250 x h = 78,55,000

h = 78,55,000 x `1/(3.142 xx 250 xx 250)`

h = 40 cm.