This figure is not drawn to scale. A rectangular glass tank 90 cm by 52 cm by 46 cm has 2 compartments, Z and A, with a water height of 36 cm in Z and 18 cm in A. A hole in the slider caused water to leak from Z to A. 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 Z to A in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Z
= 15 x 36 x 52
= 28080 cm
3 Length of Compartment A
= 90 - 15
= 75 cm
Volume of the water in Compartment A
= 75 x 52 x 18
= 70200 cm
3 Total volume of water
= 28080 + 70200
= 98280 cm
3 Base area of the glass tank
= 90 x 52
= 4680 cm
2 Height of water
= 98280 ÷ 4680
= 21 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment Z
= 36 - 21
= 15 cm
Drop in the volume of Compartment Z
= 52 x 15 x 15
= 11700 cm
3 Volume of water flowed from Z to A in 1 minute
= 11700 ÷ 75
≈ 156.0 cm
3 Answer(s): (a) 21 cm; (b) 156.0 cm
3