This figure is not drawn to scale. A rectangular glass container 75 cm by 59 cm by 43 cm has 2 compartments, A and B, with a water height of 36 cm in A and 18 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
= 35 x 36 x 59
= 74340 cm
3 Length of Compartment B
= 75 - 35
= 40 cm
Volume of the water in Compartment B
= 40 x 59 x 18
= 42480 cm
3 Total volume of water
= 74340 + 42480
= 116820 cm
3 Base area of the glass container
= 75 x 59
= 4425 cm
2 Height of water
= 116820 ÷ 4425
= 26.4 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment A
= 36 - 26.4
= 9.6 cm
Drop in the volume of Compartment A
= 59 x 35 x 9.6
= 19824 cm
3 Volume of water flowed from A to B in 1 minute
= 19824 ÷ 72
≈ 275.3 cm
3 Answer(s): (a) 26.4 cm; (b) 275.3 cm
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