This figure is not drawn to scale. A rectangular glass tank 75 cm by 57 cm by 42 cm has 2 compartments, R and S, with a water height of 30 cm in R and 10 cm in S. A hole in the slider caused water to leak from R to S. 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 112 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 R to S in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment R
= 24 x 30 x 57
= 41040 cm
3 Length of Compartment S
= 75 - 24
= 51 cm
Volume of the water in Compartment S
= 51 x 57 x 10
= 29070 cm
3 Total volume of water
= 41040 + 29070
= 70110 cm
3 Base area of the glass tank
= 75 x 57
= 4275 cm
2 Height of water
= 70110 ÷ 4275
= 16.4 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment R
= 30 - 16.4
= 13.6 cm
Drop in the volume of Compartment R
= 57 x 24 x 13.6
= 18604.8 cm
3 Volume of water flowed from R to S in 1 minute
= 18604.8 ÷ 90
≈ 206.7 cm
3 Answer(s): (a) 16.4 cm; (b) 206.7 cm
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