This figure is not drawn to scale. A rectangular glass container 80 cm by 55 cm by 45 cm has 2 compartments, U and V, with a water height of 33 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 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 U to V in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment U
= 14 x 33 x 55
= 25410 cm
3 Length of Compartment V
= 80 - 14
= 66 cm
Volume of the water in Compartment V
= 66 x 55 x 17
= 61710 cm
3 Total volume of water
= 25410 + 61710
= 87120 cm
3 Base area of the glass container
= 80 x 55
= 4400 cm
2 Height of water
= 87120 ÷ 4400
= 19.8 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment U
= 33 - 19.8
= 13.2 cm
Drop in the volume of Compartment U
= 55 x 14 x 13.2
= 10164 cm
3 Volume of water flowed from U to V in 1 minute
= 10164 ÷ 90
≈ 112.9 cm
3 Answer(s): (a) 19.8 cm; (b) 112.9 cm
3