This figure is not drawn to scale. A rectangular glass container 78 cm by 58 cm by 50 cm has 2 compartments, A and B, with a water height of 38 cm in A and 12 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 114 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 38 x 58
= 52896 cm
3 Length of Compartment B
= 78 - 24
= 54 cm
Volume of the water in Compartment B
= 54 x 58 x 12
= 37584 cm
3 Total volume of water
= 52896 + 37584
= 90480 cm
3 Base area of the glass container
= 78 x 58
= 4524 cm
2 Height of water
= 90480 ÷ 4524
= 20 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment A
= 38 - 20
= 18 cm
Drop in the volume of Compartment A
= 58 x 24 x 18
= 25056 cm
3 Volume of water flowed from A to B in 1 minute
= 25056 ÷ 75
≈ 334.1 cm
3 Answer(s): (a) 20 cm; (b) 334.1 cm
3