A rectangular water-tank measuring 80 cm x 60 cm x 60 cm is filled from a pipe of cross-sectional area 1.5 cm², the water emerging at 3.2 m/s. How long does it take to fill the tank?

Given:

Dimensions of the rectangular tank = 80 cm x 60 cm x 60 cm

Cross-sectional area of the pipe = 1.5 cm²

Speed of water = 3.2 m/s = 3.2 × 100 cm/s = 320 cm/s

Volume of the rectangular tank = 80 x 60 x 60 cm³

= 2,88,000 cm³

Volume of water flowing per second = Cross-sectional area x Speed of water

= 1.5 x 320 cm³/s

= 480 cm³/s

Volume of water flowing per minute = 480 x 60 cm³

= 28,800 cm³/min

Total time required to fill the tank = $\dfrac{\text{Volume of tank}}{\text{Volume per minute}}$

= $\dfrac{288,000}{28,800}$ min

= 10 minutes

Hence, the time taken by the pipe to fill the tank is 10 minutes.