This figure is not drawn to scale. A rectangular glass container 75 cm by 57 cm by 50 cm has 2 compartments, X and Y, with a water height of 32 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 container 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 X to Y in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment X
= 16 x 32 x 57
= 29184 cm
3 Length of Compartment Y
= 75 - 16
= 59 cm
Volume of the water in Compartment Y
= 59 x 57 x 14
= 47082 cm
3 Total volume of water
= 29184 + 47082
= 76266 cm
3 Base area of the glass container
= 75 x 57
= 4275 cm
2 Height of water
= 76266 ÷ 4275
= 17.84 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment X
= 32 - 17.84
= 14.16 cm
Drop in the volume of Compartment X
= 57 x 16 x 14.16
= 12913.92 cm
3 Volume of water flowed from X to Y in 1 minute
= 12913.92 ÷ 90
≈ 143.5 cm
3 Answer(s): (a) 17.84 cm; (b) 143.5 cm
3