This figure is not drawn to scale. A rectangular glass tank 80 cm by 56 cm by 42 cm has 2 compartments, U and V, with a water height of 33 cm in U and 16 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
= 36 x 33 x 56
= 66528 cm
3 Length of Compartment V
= 80 - 36
= 44 cm
Volume of the water in Compartment V
= 44 x 56 x 16
= 39424 cm
3 Total volume of water
= 66528 + 39424
= 105952 cm
3 Base area of the glass tank
= 80 x 56
= 4480 cm
2 Height of water
= 105952 ÷ 4480
= 23.65 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment U
= 33 - 23.65
= 9.35 cm
Drop in the volume of Compartment U
= 56 x 36 x 9.35
= 18849.6 cm
3 Volume of water flowed from U to V in 1 minute
= 18849.6 ÷ 90
≈ 209.4 cm
3 Answer(s): (a) 23.65 cm; (b) 209.4 cm
3