It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 440 cubic metres in 10 minutes. The inner radius of the pipe should be :

A. $$\sqrt 2 \,m$$

B. $$ 2 \,m$$

C. $$\frac{1}{{2 }}\,m$$

D. $$\frac{1}{{\sqrt 2 }}\,m$$

Answer: Option A

Solution(By Examveda Team)

Let the inner radius of the pipe be r metres
Then,
Volume of water flowing through the pipe in 10 minutes :
$$\eqalign{ & = \left[ {\left( {\frac{{22}}{7} \times {r^2} \times 7} \right) \times 10} \right]{m^3} \cr & = \left( {220{r^2}} \right){m^3} \cr & \therefore 220{r^2} = 440 \cr & \Rightarrow {r^2} = 2 \cr & \Rightarrow r = \sqrt 2 \, m \cr } $$