This figure is not drawn to scale. A rectangular glass tank 75 cm by 60 cm by 41 cm has 2 compartments, Y and Z, with a water height of 36 cm in Y and 11 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 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 Y to Z in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Y
= 12 x 36 x 60
= 25920 cm
3 Length of Compartment Z
= 75 - 12
= 63 cm
Volume of the water in Compartment Z
= 63 x 60 x 11
= 41580 cm
3 Total volume of water
= 25920 + 41580
= 67500 cm
3 Base area of the glass tank
= 75 x 60
= 4500 cm
2 Height of water
= 67500 ÷ 4500
= 15 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment Y
= 36 - 15
= 21 cm
Drop in the volume of Compartment Y
= 60 x 12 x 21
= 15120 cm
3 Volume of water flowed from Y to Z in 1 minute
= 15120 ÷ 105
≈ 144.0 cm
3 Answer(s): (a) 15 cm; (b) 144.0 cm
3