This figure is not drawn to scale. A rectangular glass tank 90 cm by 58 cm by 40 cm has 2 compartments, R and S, with a water height of 38 cm in R and 15 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 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 R to S in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment R
= 27 x 38 x 58
= 59508 cm
3 Length of Compartment S
= 90 - 27
= 63 cm
Volume of the water in Compartment S
= 63 x 58 x 15
= 54810 cm
3 Total volume of water
= 59508 + 54810
= 114318 cm
3 Base area of the glass tank
= 90 x 58
= 5220 cm
2 Height of water
= 114318 ÷ 5220
= 21.9 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment R
= 38 - 21.9
= 16.1 cm
Drop in the volume of Compartment R
= 58 x 27 x 16.1
= 25212.6 cm
3 Volume of water flowed from R to S in 1 minute
= 25212.6 ÷ 72
≈ 350.2 cm
3 Answer(s): (a) 21.9 cm; (b) 350.2 cm
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