Question

Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cylindrical tank, the radius of whose base is 60 cm. By how much will the level of water rise in 30 minutes? 

(a) 2 m 

(b) 3 m 

(c) 4 m 

(d) 5 m

Answer 1

(b) 3m

Length of water flown in 30 minutes = (6 × 60 × 30) m = 10800 m 

Radius of pipe = \(\frac{1}{100}\) m, h = 10800 m 

∴ Volume of water flown through the pipe

= \(\bigg(π\times\frac{1}{100}\times\frac{1}{100}\times10800\bigg)\) m³

Let h be the rise in the level of water in the tank in 30 minutes.

Then, \(π\times\frac{60}{100}\times\frac{60}{100}\times{h} \) = \(π\times\frac{1}{100}\times\frac{1}{100}\times{10800} \)

⇒ h = \(\frac{108}{100}\times\frac53\times\frac53\) = 3m.