This figure is not drawn to scale. A rectangular glass tank 75 cm by 57 cm by 47 cm has 2 compartments, U and V, with a water height of 31 cm in U and 14 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 134 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
= 33 x 31 x 57
= 58311 cm
3 Length of Compartment V
= 75 - 33
= 42 cm
Volume of the water in Compartment V
= 42 x 57 x 14
= 33516 cm
3 Total volume of water
= 58311 + 33516
= 91827 cm
3 Base area of the glass tank
= 75 x 57
= 4275 cm
2 Height of water
= 91827 ÷ 4275
= 21.48 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment U
= 31 - 21.48
= 9.52 cm
Drop in the volume of Compartment U
= 57 x 33 x 9.52
= 17907.12 cm
3 Volume of water flowed from U to V in 1 minute
= 17907.12 ÷ 105
≈ 170.5 cm
3 Answer(s): (a) 21.48 cm; (b) 170.5 cm
3