This figure is not drawn to scale. A rectangular glass tank 80 cm by 53 cm by 50 cm has 2 compartments, X and Y, with a water height of 40 cm in X and 14 cm in Y. A hole in the slider caused water to leak from X to Y. 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 114 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 X to Y in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment X
= 14 x 40 x 53
= 29680 cm
3 Length of Compartment Y
= 80 - 14
= 66 cm
Volume of the water in Compartment Y
= 66 x 53 x 14
= 48972 cm
3 Total volume of water
= 29680 + 48972
= 78652 cm
3 Base area of the glass tank
= 80 x 53
= 4240 cm
2 Height of water
= 78652 ÷ 4240
= 18.55 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment X
= 40 - 18.55
= 21.45 cm
Drop in the volume of Compartment X
= 53 x 14 x 21.45
= 15915.9 cm
3 Volume of water flowed from X to Y in 1 minute
= 15915.9 ÷ 75
≈ 212.2 cm
3 Answer(s): (a) 18.55 cm; (b) 212.2 cm
3