This figure is not drawn to scale. A rectangular glass tank 75 cm by 55 cm by 44 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 tank 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
= 28 x 37 x 55
= 56980 cm
3 Length of Compartment K
= 75 - 28
= 47 cm
Volume of the water in Compartment K
= 47 x 55 x 16
= 41360 cm
3 Total volume of water
= 56980 + 41360
= 98340 cm
3 Base area of the glass tank
= 75 x 55
= 4125 cm
2 Height of water
= 98340 ÷ 4125
= 23.84 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment J
= 37 - 23.84
= 13.16 cm
Drop in the volume of Compartment J
= 55 x 28 x 13.16
= 20266.4 cm
3 Volume of water flowed from J to K in 1 minute
= 20266.4 ÷ 72
≈ 281.5 cm
3 Answer(s): (a) 23.84 cm; (b) 281.5 cm
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