This figure is not drawn to scale. A rectangular glass tank 80 cm by 50 cm by 50 cm has 2 compartments, Y and Z, with a water height of 39 cm in Y and 19 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 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 Y to Z in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Y
= 26 x 39 x 50
= 50700 cm
3 Length of Compartment Z
= 80 - 26
= 54 cm
Volume of the water in Compartment Z
= 54 x 50 x 19
= 51300 cm
3 Total volume of water
= 50700 + 51300
= 102000 cm
3 Base area of the glass tank
= 80 x 50
= 4000 cm
2 Height of water
= 102000 ÷ 4000
= 25.5 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment Y
= 39 - 25.5
= 13.5 cm
Drop in the volume of Compartment Y
= 50 x 26 x 13.5
= 17550 cm
3 Volume of water flowed from Y to Z in 1 minute
= 17550 ÷ 90
≈ 195.0 cm
3 Answer(s): (a) 25.5 cm; (b) 195.0 cm
3