This figure is not drawn to scale. A rectangular glass container 74 cm by 51 cm by 50 cm has 2 compartments, R and S, with a water height of 33 cm in R and 13 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
= 37 x 33 x 51
= 62271 cm
3 Length of Compartment S
= 74 - 37
= 37 cm
Volume of the water in Compartment S
= 37 x 51 x 13
= 24531 cm
3 Total volume of water
= 62271 + 24531
= 86802 cm
3 Base area of the glass container
= 74 x 51
= 3774 cm
2 Height of water
= 86802 ÷ 3774
= 23 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment R
= 33 - 23
= 10 cm
Drop in the volume of Compartment R
= 51 x 37 x 10
= 18870 cm
3 Volume of water flowed from R to S in 1 minute
= 18870 ÷ 105
≈ 179.7 cm
3 Answer(s): (a) 23 cm; (b) 179.7 cm
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