This figure is not drawn to scale. A rectangular glass container 75 cm by 56 cm by 41 cm has 2 compartments, R and S, with a water height of 36 cm in R and 12 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 container now?
- It took 134 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
= 29 x 36 x 56
= 58464 cm
3 Length of Compartment S
= 75 - 29
= 46 cm
Volume of the water in Compartment S
= 46 x 56 x 12
= 30912 cm
3 Total volume of water
= 58464 + 30912
= 89376 cm
3 Base area of the glass container
= 75 x 56
= 4200 cm
2 Height of water
= 89376 ÷ 4200
= 21.28 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment R
= 36 - 21.28
= 14.72 cm
Drop in the volume of Compartment R
= 56 x 29 x 14.72
= 23905.28 cm
3 Volume of water flowed from R to S in 1 minute
= 23905.28 ÷ 105
≈ 227.7 cm
3 Answer(s): (a) 21.28 cm; (b) 227.7 cm
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