This figure is not drawn to scale. A rectangular glass tank 75 cm by 54 cm by 43 cm has 2 compartments, X and Y, with a water height of 35 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
= 27 x 35 x 54
= 51030 cm
3 Length of Compartment Y
= 75 - 27
= 48 cm
Volume of the water in Compartment Y
= 48 x 54 x 14
= 36288 cm
3 Total volume of water
= 51030 + 36288
= 87318 cm
3 Base area of the glass tank
= 75 x 54
= 4050 cm
2 Height of water
= 87318 ÷ 4050
= 21.56 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment X
= 35 - 21.56
= 13.44 cm
Drop in the volume of Compartment X
= 54 x 27 x 13.44
= 19595.52 cm
3 Volume of water flowed from X to Y in 1 minute
= 19595.52 ÷ 75
≈ 261.3 cm
3 Answer(s): (a) 21.56 cm; (b) 261.3 cm
3