This figure is not drawn to scale. A rectangular glass container 80 cm by 54 cm by 40 cm has 2 compartments, J and K, with a water height of 37 cm in J and 16 cm in K. A hole in the slider caused water to leak from J to K. 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 J to K in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment J
= 16 x 37 x 54
= 31968 cm
3 Length of Compartment K
= 80 - 16
= 64 cm
Volume of the water in Compartment K
= 64 x 54 x 16
= 55296 cm
3 Total volume of water
= 31968 + 55296
= 87264 cm
3 Base area of the glass container
= 80 x 54
= 4320 cm
2 Height of water
= 87264 ÷ 4320
= 20.2 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment J
= 37 - 20.2
= 16.8 cm
Drop in the volume of Compartment J
= 54 x 16 x 16.8
= 14515.2 cm
3 Volume of water flowed from J to K in 1 minute
= 14515.2 ÷ 72
≈ 201.6 cm
3 Answer(s): (a) 20.2 cm; (b) 201.6 cm
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