Mathematics

Problem

An overhead right circular cylindrical water tank has an internal radius of

1\,\text{m}

and an internal height of

3.5\,\text{m}

. Water is pumped into the tank at the rate of

25\,\text{litres per second}

, but due to a leakage at the bottom, water simultaneously flows out at

5\,\text{litres per second}

. Initially, the tank is empty. a. (i) Find the net rate at which the volume of water in the tank increases. b. (ii) The tank is considered full when the water level reaches a height that is

5\,\text{cm}

below the rim. Determine the time required, in minutes and seconds, to fill the tank to this level. Use

\pi = \dfrac{22}{7}

and

1\,\text{m}^3 = 1000\,\text{L}

. Give your answer correct to the nearest second.

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