This figure is not drawn to scale. A rectangular glass tank 72 cm by 57 cm by 48 cm has 2 compartments, Z and A, with a water height of 40 cm in Z and 14 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 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 Z to A in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Z
= 27 x 40 x 57
= 61560 cm
3 Length of Compartment A
= 72 - 27
= 45 cm
Volume of the water in Compartment A
= 45 x 57 x 14
= 35910 cm
3 Total volume of water
= 61560 + 35910
= 97470 cm
3 Base area of the glass tank
= 72 x 57
= 4104 cm
2 Height of water
= 97470 ÷ 4104
= 23.75 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment Z
= 40 - 23.75
= 16.25 cm
Drop in the volume of Compartment Z
= 57 x 27 x 16.25
= 25008.75 cm
3 Volume of water flowed from Z to A in 1 minute
= 25008.75 ÷ 90
≈ 277.9 cm
3 Answer(s): (a) 23.75 cm; (b) 277.9 cm
3