This figure is not drawn to scale. A rectangular glass container 76 cm by 56 cm by 49 cm has 2 compartments, Q and R, with a water height of 34 cm in Q and 15 cm in R. A hole in the slider caused water to leak from Q to R. 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 112 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 Q to R in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Q
= 17 x 34 x 56
= 32368 cm
3 Length of Compartment R
= 76 - 17
= 59 cm
Volume of the water in Compartment R
= 59 x 56 x 15
= 49560 cm
3 Total volume of water
= 32368 + 49560
= 81928 cm
3 Base area of the glass container
= 76 x 56
= 4256 cm
2 Height of water
= 81928 ÷ 4256
= 19.25 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment Q
= 34 - 19.25
= 14.75 cm
Drop in the volume of Compartment Q
= 56 x 17 x 14.75
= 14042 cm
3 Volume of water flowed from Q to R in 1 minute
= 14042 ÷ 90
≈ 156 cm
3 Answer(s): (a) 19.25 cm; (b) 156 cm
3