Question

A swimming pool 70 m X 44 m X 3m is filled by water issuing a pipe of diameter 35 cm at 6 m per second.How many hours does it make to fill the pool?

Answer 1

Given :

Length of a swimming pool(l)= 70 m

Breadth of a swimming pool(b)= 44 m

Height of a swimming pool(h)= 3 m

Diameter of pipe(d)=35 cm=

Radius of pipe(r) = d/2= 35/2= 17.5 cm= 17.5/100= .175 m

Length of water(h) flowing in a pipe in x seconds = 6 x

Capacity of swimming pool= l× b×h

Volume of pipe = πr²h

Volume of water flowing through a cylindrical pipe =Capacity of swimming pool

πr²h= l× b×h

22/7×(.175)²×6 × x =70×44×3

22/7×.175 × .175×6x =70×44×3

x= (70× 44× 3× 7) / ( 22× .175× .175 × 6)

x= 10000000/25×25= 10000000/625

x= 16000 sec

x= 16000/3600 hrs

x= 40/9 hrs= 4 4/9 hrs

Hence,the pipe takes in fraction 4 4/9 hrs to fill the swimming pool