Mathematics

Problem

The circumference of the base of a cylindrical water tank is

8.8\,\text{m}

. The depth of the tank is

3.5\,\text{m}

. Water is supplied through a pipe that discharges at the rate of

50\,\text{litres per second}

. a. (i) Find the radius of the base of the tank. b. (ii) Calculate the capacity of the tank in cubic metres. c. (iii) Convert the capacity into litres. d. (iv) Determine the time, in minutes, required to fill the empty tank completely with the given pipe.

Intuitive explanation

This problem combines geometry and rates—you need to find how much space the cylinder holds, then figure out how long it takes to fill that volume at a constant flow rate. Start by recovering the radius from the circumference, then calculate the tank's volume using the cylinder formula $V = \pi r^2 h$ . Once you have the total capacity in cubic meters, convert to liters and divide by the discharge rate to find the time.

Intuitive explanation

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