This figure is not drawn to scale. A rectangular glass container 75 cm by 56 cm by 47 cm has 2 compartments, R and S, with a water height of 34 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
= 28 x 34 x 56
= 53312 cm
3 Length of Compartment S
= 75 - 28
= 47 cm
Volume of the water in Compartment S
= 47 x 56 x 13
= 34216 cm
3 Total volume of water
= 53312 + 34216
= 87528 cm
3 Base area of the glass container
= 75 x 56
= 4200 cm
2 Height of water
= 87528 ÷ 4200
= 20.84 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment R
= 34 - 20.84
= 13.16 cm
Drop in the volume of Compartment R
= 56 x 28 x 13.16
= 20634.88 cm
3 Volume of water flowed from R to S in 1 minute
= 20634.88 ÷ 105
≈ 196.5 cm
3 Answer(s): (a) 20.84 cm; (b) 196.5 cm
3