Question

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled ?

Answer 1

Internal diameter of a pipe \(=20 \mathrm{~cm}\).
Radius of pipe \(=10 \mathrm{~cm} .=\frac{1}{10} \mathrm{~m}\)
Diameter of cylindrical tank \(=10 \mathrm{~m} ; \mathrm{r}=5 \mathrm{~m}\).
Depth of cylindrical tank \(=2 \mathrm{~m}\).
Speed of water is \(3 \mathrm{~km} / \mathrm{hr}\).
Time required to fill the water tank =?
Speed of water \(=3 \mathrm{~km} / \mathrm{hr}\).
$$
\begin{aligned}
&=\frac{3000}{60} \mathrm{~m} / \text { minute } \\
&=50 \mathrm{~m} / \mathrm{min} .
\end{aligned}
$$
Let time required to fill the tank be n' minutes.
\(\therefore\) Flowing water in 'n' minutes = Volume of water tank
$$
\begin{gathered}
\Rightarrow \pi \times\left(\frac{1}{10}\right)^{2} \times(n \times 50)=\pi \times(5)^{2} \times 2 \\
\frac{1}{100} n \times 50=50 \\
\therefore n=100 \text { minutes }
\end{gathered}
$$
\(\therefore\) Time required to fill the water tank \(=100\) minutes

Answer 2

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Answer 3

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