This figure is not drawn to scale. A rectangular glass container 70 cm by 58 cm by 43 cm has 2 compartments, R and S, with a water height of 40 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 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
= 16 x 40 x 58
= 37120 cm
3 Length of Compartment S
= 70 - 16
= 54 cm
Volume of the water in Compartment S
= 54 x 58 x 12
= 37584 cm
3 Total volume of water
= 37120 + 37584
= 74704 cm
3 Base area of the glass container
= 70 x 58
= 4060 cm
2 Height of water
= 74704 ÷ 4060
= 18.4 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment R
= 40 - 18.4
= 21.6 cm
Drop in the volume of Compartment R
= 58 x 16 x 21.6
= 20044.8 cm
3 Volume of water flowed from R to S in 1 minute
= 20044.8 ÷ 72
≈ 278.4 cm
3 Answer(s): (a) 18.4 cm; (b) 278.4 cm
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