Question

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

• A. $50$ minutes
• B. $50$minutes $1$ seconds
• C. $51$minutes $12$ seconds
• D. $51$minutes $15$ seconds

Answer 1

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

Volume of conical$=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \pi \times 20\times 20\times 24$

$=3200\pi$

Volume of water flows per minute$=\pi r^2\times 10=\pi \times \frac{2.5}{10}\times \frac{2.5}{10}\times 1000$

$=62.5\pi$

Time taken$=\frac{3200\pi }{62.5\pi }=51.2$ min $=51$ min $12$ sec.