This figure is not drawn to scale. A rectangular glass container 75 cm by 56 cm by 50 cm has 2 compartments, J and K, with a water height of 31 cm in J and 15 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
= 36 x 31 x 56
= 62496 cm
3 Length of Compartment K
= 75 - 36
= 39 cm
Volume of the water in Compartment K
= 39 x 56 x 15
= 32760 cm
3 Total volume of water
= 62496 + 32760
= 95256 cm
3 Base area of the glass container
= 75 x 56
= 4200 cm
2 Height of water
= 95256 ÷ 4200
= 22.68 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment J
= 31 - 22.68
= 8.32 cm
Drop in the volume of Compartment J
= 56 x 36 x 8.32
= 16773.12 cm
3 Volume of water flowed from J to K in 1 minute
= 16773.12 ÷ 72
≈ 233 cm
3 Answer(s): (a) 22.68 cm; (b) 233 cm
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