This figure is not drawn to scale. A rectangular glass container 70 cm by 60 cm by 49 cm has 2 compartments, A and B, with a water height of 40 cm in A and 19 cm in B. A hole in the slider caused water to leak from A to B. 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 A to B in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment A
= 24 x 40 x 60
= 57600 cm
3 Length of Compartment B
= 70 - 24
= 46 cm
Volume of the water in Compartment B
= 46 x 60 x 19
= 52440 cm
3 Total volume of water
= 57600 + 52440
= 110040 cm
3 Base area of the glass container
= 70 x 60
= 4200 cm
2 Height of water
= 110040 ÷ 4200
= 26.2 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment A
= 40 - 26.2
= 13.8 cm
Drop in the volume of Compartment A
= 60 x 24 x 13.8
= 19872 cm
3 Volume of water flowed from A to B in 1 minute
= 19872 ÷ 90
≈ 220.8 cm
3 Answer(s): (a) 26.2 cm; (b) 220.8 cm
3