This figure is not drawn to scale. A rectangular glass tank 75 cm by 55 cm by 43 cm has 2 compartments, U and V, with a water height of 40 cm in U and 12 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 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
= 36 x 40 x 55
= 79200 cm
3 Length of Compartment V
= 75 - 36
= 39 cm
Volume of the water in Compartment V
= 39 x 55 x 12
= 25740 cm
3 Total volume of water
= 79200 + 25740
= 104940 cm
3 Base area of the glass tank
= 75 x 55
= 4125 cm
2 Height of water
= 104940 ÷ 4125
= 25.44 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment U
= 40 - 25.44
= 14.56 cm
Drop in the volume of Compartment U
= 55 x 36 x 14.56
= 28828.8 cm
3 Volume of water flowed from U to V in 1 minute
= 28828.8 ÷ 75
≈ 384.4 cm
3 Answer(s): (a) 25.44 cm; (b) 384.4 cm
3