This figure is not drawn to scale. A rectangular glass tank 85 cm by 55 cm by 43 cm has 2 compartments, W and X, with a water height of 36 cm in W and 19 cm in X. A hole in the slider caused water to leak from W to X. 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 W to X in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment W
= 24 x 36 x 55
= 47520 cm
3 Length of Compartment X
= 85 - 24
= 61 cm
Volume of the water in Compartment X
= 61 x 55 x 19
= 63745 cm
3 Total volume of water
= 47520 + 63745
= 111265 cm
3 Base area of the glass tank
= 85 x 55
= 4675 cm
2 Height of water
= 111265 ÷ 4675
= 23.8 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment W
= 36 - 23.8
= 12.2 cm
Drop in the volume of Compartment W
= 55 x 24 x 12.2
= 16104 cm
3 Volume of water flowed from W to X in 1 minute
= 16104 ÷ 105
≈ 153.4 cm
3 Answer(s): (a) 23.8 cm; (b) 153.4 cm
3