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Water flows at the rate of 10m/minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

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\text{The diameter of the conical vessel}= 40cm

Radius= \frac{40cm}{2} = 20cm


Volume=\frac{1}{3}\pi r^2 h=\frac{1}{3}\pi\times20\times20\times24 = 3200\pi cm^3

Diameter of water that flows out of cylinder = 5mm


(Because 1 cm = 10mm)

Height=10m=1000cm        ( Because 1m =100cm)

\text{Volume}=\pi r^2h=\pi\times\frac{5}{20}\times\frac{5}{20}\times1000\Rightarrow \frac{125}{2}\pi cm^3

\text{Time required}=\frac{\text {volume of conical flask}}{\text{volume of cylindrical water}}=\frac{3200\pi}{125\pi}\times2

\Rightarrow \frac{640\times2}{25}\Rightarrow \frac{1280}{25}=51.2\ minutes


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