This figure is not drawn to scale. A rectangular glass container 80 cm by 60 cm by 41 cm has 2 compartments, J and K, with a water height of 36 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
= 24 x 36 x 60
= 51840 cm
3 Length of Compartment K
= 80 - 24
= 56 cm
Volume of the water in Compartment K
= 56 x 60 x 16
= 53760 cm
3 Total volume of water
= 51840 + 53760
= 105600 cm
3 Base area of the glass container
= 80 x 60
= 4800 cm
2 Height of water
= 105600 ÷ 4800
= 22 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment J
= 36 - 22
= 14 cm
Drop in the volume of Compartment J
= 60 x 24 x 14
= 20160 cm
3 Volume of water flowed from J to K in 1 minute
= 20160 ÷ 72
≈ 280.0 cm
3 Answer(s): (a) 22 cm; (b) 280.0 cm
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