Question

Water flows, at 9 km per hour, through a cylindrical pipe of cross-sectional area 25 cm². If this water is collected into a rectangular cistern of dimensions 7.5 m by 5 m by 4 m; calculate the rise in level in the cistern in 1 hour 15 minutes.

Answer 1

Rate of flow of water = 9 km/hr

Water flow in 1 hour 15 minutes 

i.e. in `5/4 hr = 9 xx 5/4`

= `45/4 km`

= `45/4 xx 1000`

= 11250 m 

Area of cross-section

= 25 cm²

= `25/10000 m^2`

= `1/400 m^2` 

Therefore, volume of water

= `1/400 xx 11250`

= 28.125 m³

Dimensions of water tank = 7.5 m × 5 m × 4 m 

Area of tank = l × b

= 7.5 × 5

= 37.5 m²

Let h be the height of water then, 

37.5 × h = 28.125 

`h = 28.125/37.5`

= 0.75 m

= 75 cm