This figure is not drawn to scale. A rectangular glass container 70 cm by 57 cm by 48 cm has 2 compartments, Z and A, with a water height of 40 cm in Z and 12 cm in A. A hole in the slider caused water to leak from Z to A. 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 112 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 Z to A in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Z
= 28 x 40 x 57
= 63840 cm
3 Length of Compartment A
= 70 - 28
= 42 cm
Volume of the water in Compartment A
= 42 x 57 x 12
= 28728 cm
3 Total volume of water
= 63840 + 28728
= 92568 cm
3 Base area of the glass container
= 70 x 57
= 3990 cm
2 Height of water
= 92568 ÷ 3990
= 23.2 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment Z
= 40 - 23.2
= 16.8 cm
Drop in the volume of Compartment Z
= 57 x 28 x 16.8
= 26812.8 cm
3 Volume of water flowed from Z to A in 1 minute
= 26812.8 ÷ 90
≈ 297.9 cm
3 Answer(s): (a) 23.2 cm; (b) 297.9 cm
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