Question

water is a flowing at the rate of 5km per hour through a pipe of diameter 14cm into a rectangular tank of base 30m × 22m. find the time during which the level of water in the tank rises by 35cm​

Answer 1

GIVEN -

water flowing at the rate of = 5km/hr

pipe of radius = 14/2 = 7 cm = 7/100 m

rectangular tank of base = 30 m

rectangular tank of length = 22m

water rise = height = 35 cm = 35/100 m

TO FIND -

Time at which the level of water reaches 35cm.

SOLUTION -

=》Let the level of water in the tank will rise by 35 cm in x hrs

=》As the rate of flow of water is 5km/hr.

∴ Its length in x hrs = 5x=5000x metres,

=》Water column forms a cylinder whose radius is

⇒r = 14/2 = 7 cm = 7/100 m

=》Volume of water flowing through the cylindrical pipe in x hrs

= $\pi {r}^{2} h$

= 22/7 × (7/100)² × 5000x

= 77 xm³

=》Vol. of water that falls into tank = l × b × h

= 30 × 22 × 35/100

= 231 m³

=》But, the volume of water flowing through the cylindrical pipe in x hrs = Vol. of water that falls in a tank in x hrs.

⇒77x= 231

∴ x = 231/77

=》x = 3 hr.

HENCE THE TIME TAKEN BY PIPE TO FILL THE WATER TANK BY 35 CM IS 3HRS..