Question

Water flows at the rate of $10$ cubic mm per minute from a cylindrical pipe $5$ mm in diameter. A conical vessel, whose diameter at the base is $40$ cm and depth $24$ cm, is filled. The time taken to fill the conical vessel is

• A. $50$ minutes
• B. $50$ minutes $12$ seconds
• C. $51$ minutes $12$ seconds
• D. $50$ minutes $15$ seconds

Answer 1

The correct option is C $51$ minutes $12$ seconds

Volume of water per minute

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

$=\pi {\left(\frac{5}{2}\right)}^2\times 10\times 100\times 10$

$=\frac{25\times 100\times 100}{4}\pi m{m}^3$

Volume of conical vessel
$=\frac{1}{3}\pi (200{)}^2\times 240$
$\therefore$ time taken $=\frac{\frac{1}{3}\pi \times 200\times 200\times 240}{25\times 100\times 100\times \pi }\times 4$

$=\frac{3840}{75}$ minutes

$=$ $51$ minutes $12$ seconds