This figure is not drawn to scale. A rectangular glass tank 75 cm by 50 cm by 41 cm has 2 compartments, U and V, with a water height of 34 cm in U and 15 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 tank 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
= 15 x 34 x 50
= 25500 cm
3 Length of Compartment V
= 75 - 15
= 60 cm
Volume of the water in Compartment V
= 60 x 50 x 15
= 45000 cm
3 Total volume of water
= 25500 + 45000
= 70500 cm
3 Base area of the glass tank
= 75 x 50
= 3750 cm
2 Height of water
= 70500 ÷ 3750
= 18.8 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment U
= 34 - 18.8
= 15.2 cm
Drop in the volume of Compartment U
= 50 x 15 x 15.2
= 11400 cm
3 Volume of water flowed from U to V in 1 minute
= 11400 ÷ 90
≈ 126.7 cm
3 Answer(s): (a) 18.8 cm; (b) 126.7 cm
3