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Question 75

The radius of a cylinderical cistern is 10 m and its height is 15 m. Initially the cistern is empty. We start filling the cistern with water through a pipe whose diameter is 50 cm. Water is coming out of the pipe with a velocity of 5 m/s. How many minutes will it take in filling the cistern with water?

Solution

Radius of cistern $$R=10m$$ and height = $$H=15$$ m

Radius of cylindrical pipe $$r=0.25m$$ and height = $$h=5$$ m (for 1 sec)

=> Volume of cylindrical cistern = $$\pi r^2h$$

$$\therefore$$ Time taken to fill the cistern (in minutes) = $$\frac{\pi (10)^2\times15}{\pi\times(0.25)^2\times5}\times\frac{1}{60}$$

= $$\frac{100\times10000}{625\times5\times4}$$

= $$5\times16=80$$ minutes

=> Ans - (D)

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