Question

Water flows through a cylindrical pipe of internal diameter $7$ cm at $2$ m per second. What is the volume of water (in litres) discharged in $10$ minutes?

• A. $4620$
• B. $3850$
• C. $7698$
• D. $9240$

Answer 1

The correct option is A $4620$

Given, diameter ($d$)=$7$ cm

Therefore, radius ($r$) $=$ $\frac{7}{2}$ cm

Water is flowing out at a speed of $2$ m/s.

In $10$ minutes water flows through a distance of $l$,

where, $l$ $=$ $\text{speed}\times \text{time}$

$\Rightarrow$ $l=2\times 10\times 60$ m

$\Rightarrow$ $l=1200$ m $=12\times {10}^4$ cm

Now it can be considered as a cylinder of length $12\times {10}^4$ cm and $\frac{7}{2}$ cm radius.

Therefore, volume discharged $=$ volume of cylinder

Volume of cylinder $=$ $V$ $=$ $\pi r^{2}l$

$\Rightarrow$ $V=\frac{22}{7}\times {\left(\frac{7}{2}\right)}^2\times 12\times {10}^4$ ${\text{cm}}^3$

$\Rightarrow$ $V=\frac{22}{7}\times {\left(\frac{7}{2}\right)}^2\times 12\times 10$ litres ($\because 1$ litre $=1000{\text{cm}}^3$)

Thus volume discharged, $V=4620{\text{cm}}^3$

Therefore, option C is correct