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 :
Options:
A .  $$\sqrt 2 \,m$$
B .  $$ 2 \,m$$
C .  $$\frac{1}{{2 }}\,m$$
D .  $$\frac{1}{{\sqrt 2 }}\,m$$
Answer: Option A Let the inner radius of the pipe be r metres Then, Volume of water flowing through the pipe in 10 minutes : $$\eqalign{ & = \left[ {\left( {\frac{{22}}{7} \times {r^2} \times 7} \right) \times 10} \right]{m^3} \cr & = \left( {220{r^2}} \right){m^3} \cr & \therefore 220{r^2} = 440 \cr & \Rightarrow {r^2} = 2 \cr & \Rightarrow r = \sqrt 2 \, m \cr } $$
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