This figure is not drawn to scale. A rectangular glass container 72 cm by 55 cm by 42 cm has 2 compartments, W and X, with a water height of 35 cm in W and 13 cm in X. A hole in the slider caused water to leak from W to X. 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 W to X in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment W
= 36 x 35 x 55
= 69300 cm
3 Length of Compartment X
= 72 - 36
= 36 cm
Volume of the water in Compartment X
= 36 x 55 x 13
= 25740 cm
3 Total volume of water
= 69300 + 25740
= 95040 cm
3 Base area of the glass container
= 72 x 55
= 3960 cm
2 Height of water
= 95040 ÷ 3960
= 24 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment W
= 35 - 24
= 11 cm
Drop in the volume of Compartment W
= 55 x 36 x 11
= 21780 cm
3 Volume of water flowed from W to X in 1 minute
= 21780 ÷ 72
≈ 302.5 cm
3 Answer(s): (a) 24 cm; (b) 302.5 cm
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