This figure is not drawn to scale. A rectangular glass tank 85 cm by 58 cm by 45 cm has 2 compartments, Y and Z, with a water height of 32 cm in Y and 15 cm in Z. A hole in the slider caused water to leak from Y to Z. 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 Y to Z in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Y
= 26 x 32 x 58
= 48256 cm
3 Length of Compartment Z
= 85 - 26
= 59 cm
Volume of the water in Compartment Z
= 59 x 58 x 15
= 51330 cm
3 Total volume of water
= 48256 + 51330
= 99586 cm
3 Base area of the glass tank
= 85 x 58
= 4930 cm
2 Height of water
= 99586 ÷ 4930
= 20.2 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment Y
= 32 - 20.2
= 11.8 cm
Drop in the volume of Compartment Y
= 58 x 26 x 11.8
= 17794.4 cm
3 Volume of water flowed from Y to Z in 1 minute
= 17794.4 ÷ 75
≈ 237.3 cm
3 Answer(s): (a) 20.2 cm; (b) 237.3 cm
3