This figure is not drawn to scale. A rectangular glass container 72 cm by 56 cm by 45 cm has 2 compartments, J and K, with a water height of 38 cm in J and 17 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
= 30 x 38 x 56
= 63840 cm
3 Length of Compartment K
= 72 - 30
= 42 cm
Volume of the water in Compartment K
= 42 x 56 x 17
= 39984 cm
3 Total volume of water
= 63840 + 39984
= 103824 cm
3 Base area of the glass container
= 72 x 56
= 4032 cm
2 Height of water
= 103824 ÷ 4032
= 25.75 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment J
= 38 - 25.75
= 12.25 cm
Drop in the volume of Compartment J
= 56 x 30 x 12.25
= 20580 cm
3 Volume of water flowed from J to K in 1 minute
= 20580 ÷ 72
≈ 285.8 cm
3 Answer(s): (a) 25.75 cm; (b) 285.8 cm
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