This figure is not drawn to scale. A rectangular glass container 88 cm by 58 cm by 40 cm has 2 compartments, P and Q, with a water height of 37 cm in P and 15 cm in Q. A hole in the slider caused water to leak from P to Q. 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 134 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 P to Q in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment P
= 15 x 37 x 58
= 32190 cm
3 Length of Compartment Q
= 88 - 15
= 73 cm
Volume of the water in Compartment Q
= 73 x 58 x 15
= 63510 cm
3 Total volume of water
= 32190 + 63510
= 95700 cm
3 Base area of the glass container
= 88 x 58
= 5104 cm
2 Height of water
= 95700 ÷ 5104
= 18.75 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment P
= 37 - 18.75
= 18.25 cm
Drop in the volume of Compartment P
= 58 x 15 x 18.25
= 15877.5 cm
3 Volume of water flowed from P to Q in 1 minute
= 15877.5 ÷ 105
≈ 151.2 cm
3 Answer(s): (a) 18.75 cm; (b) 151.2 cm
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