A water tank is in the form of a cube of side 2 m. It has an inlet in the shape of a circle with radius 3.5 cm. How long will it take to fill the tank (approximately), if the water is flowing at a speed of 2 m/s ?

The water tank is a cube with side length 2 m

Inlet is a circular opening with radius 3.5 cm (0.035 m).

Speed of water flow = 2 m/s

Volume of the tank (cube) = $$s^3$$​​

Area of circular inlet = $$\pi r^2$$​​

Volume flow rate = Area of inlet × Speed of water flow

Volume of tank = 2³ = 8 m³

Area of circular inlet = $$\frac{22}{7} \times {0.035}\times {0.035} = 22 \times 0.005 \times 0.035 = 0.00385\, m^2$$​​

Volume flow rate = Area × Speed = 0.00385 × 2 = 0.0077

Time to fill the tank:

Time = $$\frac{\text{Volume of tank}}{\text{Volume flow rate}}$$​​

= $$\frac{8}{0.0077} \approx 1038.96 \, \text{s} \approx 17.32 \, \text{minutes}$$​​

Thus, it will take approximately 17.32 minutes to fill the tank.