This figure is not drawn to scale. A rectangular glass tank 72 cm by 51 cm by 40 cm has 2 compartments, P and Q, with a water height of 31 cm in P and 13 cm in Q. A hole in the slider caused water to leak from P to Q. 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 P to Q in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment P
= 22 x 31 x 51
= 34782 cm
3 Length of Compartment Q
= 72 - 22
= 50 cm
Volume of the water in Compartment Q
= 50 x 51 x 13
= 33150 cm
3 Total volume of water
= 34782 + 33150
= 67932 cm
3 Base area of the glass tank
= 72 x 51
= 3672 cm
2 Height of water
= 67932 ÷ 3672
= 18.5 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment P
= 31 - 18.5
= 12.5 cm
Drop in the volume of Compartment P
= 51 x 22 x 12.5
= 14025 cm
3 Volume of water flowed from P to Q in 1 minute
= 14025 ÷ 90
≈ 155.8 cm
3 Answer(s): (a) 18.5 cm; (b) 155.8 cm
3