This figure is not drawn to scale. A rectangular glass container 90 cm by 52 cm by 50 cm has 2 compartments, R and S, with a water height of 38 cm in R and 17 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
= 15 x 38 x 52
= 29640 cm
3 Length of Compartment S
= 90 - 15
= 75 cm
Volume of the water in Compartment S
= 75 x 52 x 17
= 66300 cm
3 Total volume of water
= 29640 + 66300
= 95940 cm
3 Base area of the glass container
= 90 x 52
= 4680 cm
2 Height of water
= 95940 ÷ 4680
= 20.5 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment R
= 38 - 20.5
= 17.5 cm
Drop in the volume of Compartment R
= 52 x 15 x 17.5
= 13650 cm
3 Volume of water flowed from R to S in 1 minute
= 13650 ÷ 105
≈ 130.0 cm
3 Answer(s): (a) 20.5 cm; (b) 130.0 cm
3