This figure is not drawn to scale. A rectangular glass container 85 cm by 60 cm by 45 cm has 2 compartments, U and V, with a water height of 34 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
= 16 x 34 x 60
= 32640 cm
3 Length of Compartment V
= 85 - 16
= 69 cm
Volume of the water in Compartment V
= 69 x 60 x 17
= 70380 cm
3 Total volume of water
= 32640 + 70380
= 103020 cm
3 Base area of the glass container
= 85 x 60
= 5100 cm
2 Height of water
= 103020 ÷ 5100
= 20.2 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment U
= 34 - 20.2
= 13.8 cm
Drop in the volume of Compartment U
= 60 x 16 x 13.8
= 13248 cm
3 Volume of water flowed from U to V in 1 minute
= 13248 ÷ 90
≈ 147.2 cm
3 Answer(s): (a) 20.2 cm; (b) 147.2 cm
3