This figure is not drawn to scale. A rectangular glass tank 75 cm by 57 cm by 49 cm has 2 compartments, Y and Z, with a water height of 30 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
= 30 x 30 x 57
= 51300 cm
3 Length of Compartment Z
= 75 - 30
= 45 cm
Volume of the water in Compartment Z
= 45 x 57 x 15
= 38475 cm
3 Total volume of water
= 51300 + 38475
= 89775 cm
3 Base area of the glass tank
= 75 x 57
= 4275 cm
2 Height of water
= 89775 ÷ 4275
= 21 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment Y
= 30 - 21
= 9 cm
Drop in the volume of Compartment Y
= 57 x 30 x 9
= 15390 cm
3 Volume of water flowed from Y to Z in 1 minute
= 15390 ÷ 75
≈ 205.2 cm
3 Answer(s): (a) 21 cm; (b) 205.2 cm
3