This figure is not drawn to scale. A rectangular glass container 72 cm by 59 cm by 40 cm has 2 compartments, A and B, with a water height of 37 cm in A and 19 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 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 A to B in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment A
= 10 x 37 x 59
= 21830 cm
3 Length of Compartment B
= 72 - 10
= 62 cm
Volume of the water in Compartment B
= 62 x 59 x 19
= 69502 cm
3 Total volume of water
= 21830 + 69502
= 91332 cm
3 Base area of the glass container
= 72 x 59
= 4248 cm
2 Height of water
= 91332 ÷ 4248
= 21.5 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment A
= 37 - 21.5
= 15.5 cm
Drop in the volume of Compartment A
= 59 x 10 x 15.5
= 9145 cm
3 Volume of water flowed from A to B in 1 minute
= 9145 ÷ 105
≈ 87.1 cm
3 Answer(s): (a) 21.5 cm; (b) 87.1 cm
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