This figure is not drawn to scale. A rectangular glass tank 75 cm by 55 cm by 41 cm has 2 compartments, T and U, with a water height of 33 cm in T and 12 cm in U. A hole in the slider caused water to leak from T to U. It was found that the water level in both compartments became the same after some time.
- What is the height of water in the tank now?
- It took 112 h for the water in both compartments to reach the same level. Assuming that water leaked at a constant rate, how much water flowed from T to U in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment T
= 39 x 33 x 55
= 70785 cm
3 Length of Compartment U
= 75 - 39
= 36 cm
Volume of the water in Compartment U
= 36 x 55 x 12
= 23760 cm
3 Total volume of water
= 70785 + 23760
= 94545 cm
3 Base area of the glass tank
= 75 x 55
= 4125 cm
2 Height of water
= 94545 ÷ 4125
= 22.92 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment T
= 33 - 22.92
= 10.08 cm
Drop in the volume of Compartment T
= 55 x 39 x 10.08
= 21621.6 cm
3 Volume of water flowed from T to U in 1 minute
= 21621.6 ÷ 90
≈ 240.2 cm
3 Answer(s): (a) 22.92 cm; (b) 240.2 cm
3