Question

Water flows at the rate of $10$ meters per minute through a cylinder cylindrical pipe $5$ mm in diameter.How long would it take to fill a conical vessel whose diameter at the surface $40$$cm$ and depth $24$ cm is

• A. $61min12sec$
• B. $41min12sec$
• C. $51min12sec$
• D. $31min12sec$

Answer 1

The correct option is C $51min12sec$

$\left(LetfillConicalVesselintmin\right)Volumeofpipe=VolumeofconicalVessel$
$\Rightarrow \pi \times \frac{5\times 5}{2\times 10\times 2\times 10}\times 103/min=\frac{1}{3}\times \pi \times 20\times 20\times 24/time$
$\Rightarrow \frac{25\times 10}{4}=\frac{1}{3}\times 20\times 20\times \frac{24}{time}$
$\Rightarrow time=\frac{8\times 20\times 20\times 4}{10\times 25}$
$\Rightarrow time=\frac{64\times 20}{25}=\frac{64\times 4}{5}min$
$\Rightarrow time=51min2\sec$