This figure is not drawn to scale. A rectangular glass container 75 cm by 53 cm by 44 cm has 2 compartments, A and B, with a water height of 32 cm in A and 16 cm in B. A hole in the slider caused water to leak from A to B. 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 115 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 A to B in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment A
= 21 x 32 x 53
= 35616 cm
3 Length of Compartment B
= 75 - 21
= 54 cm
Volume of the water in Compartment B
= 54 x 53 x 16
= 45792 cm
3 Total volume of water
= 35616 + 45792
= 81408 cm
3 Base area of the glass container
= 75 x 53
= 3975 cm
2 Height of water
= 81408 ÷ 3975
= 20.48 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment A
= 32 - 20.48
= 11.52 cm
Drop in the volume of Compartment A
= 53 x 21 x 11.52
= 12821.76 cm
3 Volume of water flowed from A to B in 1 minute
= 12821.76 ÷ 72
≈ 178.1 cm
3 Answer(s): (a) 20.48 cm; (b) 178.1 cm
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