This figure is not drawn to scale. A rectangular glass container 75 cm by 53 cm by 46 cm has 2 compartments, U and V, with a water height of 38 cm in U and 17 cm in V. A hole in the slider caused water to leak from U to V. 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 U to V in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment U
= 10 x 38 x 53
= 20140 cm
3 Length of Compartment V
= 75 - 10
= 65 cm
Volume of the water in Compartment V
= 65 x 53 x 17
= 58565 cm
3 Total volume of water
= 20140 + 58565
= 78705 cm
3 Base area of the glass container
= 75 x 53
= 3975 cm
2 Height of water
= 78705 ÷ 3975
= 19.8 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment U
= 38 - 19.8
= 18.2 cm
Drop in the volume of Compartment U
= 53 x 10 x 18.2
= 9646 cm
3 Volume of water flowed from U to V in 1 minute
= 9646 ÷ 75
≈ 128.6 cm
3 Answer(s): (a) 19.8 cm; (b) 128.6 cm
3