This figure is not drawn to scale. A rectangular glass container 75 cm by 53 cm by 46 cm has 2 compartments, R and S, with a water height of 38 cm in R and 11 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
= 35 x 38 x 53
= 70490 cm
3 Length of Compartment S
= 75 - 35
= 40 cm
Volume of the water in Compartment S
= 40 x 53 x 11
= 23320 cm
3 Total volume of water
= 70490 + 23320
= 93810 cm
3 Base area of the glass container
= 75 x 53
= 3975 cm
2 Height of water
= 93810 ÷ 3975
= 23.6 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment R
= 38 - 23.6
= 14.4 cm
Drop in the volume of Compartment R
= 53 x 35 x 14.4
= 26712 cm
3 Volume of water flowed from R to S in 1 minute
= 26712 ÷ 72
≈ 371.0 cm
3 Answer(s): (a) 23.6 cm; (b) 371.0 cm
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