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1. The number of circular pipes with an inside diameter of 1 inch which will carry the same amount of water as a pipe with an inside diameter of 6 inches is :

A. $6 π$

B. $12$

C. $36$

D. $36 π$

Solution:

Let the length of each pipe be

l

inches
Then, volume of water in thinner pipe :

\begin{aligned} = [π \times {(\frac{1}{2})}^{2} \times 1] cu.inch \\ = (\frac{π l}{4}) cu.inch \end{aligned}

Volume of water in thinker pipe :

\begin{aligned} = (π \times 3^{2} \times l) cu.inch \\ = (9 π l) cu.inch \end{aligned}

∴ Required number of pipes :

\begin{aligned} = \frac{9 π l}{(\frac{π l}{4})} \\ = 36 \end{aligned}

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