This figure is not drawn to scale. A rectangular glass tank 85 cm by 54 cm by 42 cm has 2 compartments, Z and A, with a water height of 34 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 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
= 34 x 34 x 54
= 62424 cm
3 Length of Compartment A
= 85 - 34
= 51 cm
Volume of the water in Compartment A
= 51 x 54 x 14
= 38556 cm
3 Total volume of water
= 62424 + 38556
= 100980 cm
3 Base area of the glass tank
= 85 x 54
= 4590 cm
2 Height of water
= 100980 ÷ 4590
= 22 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment Z
= 34 - 22
= 12 cm
Drop in the volume of Compartment Z
= 54 x 34 x 12
= 22032 cm
3 Volume of water flowed from Z to A in 1 minute
= 22032 ÷ 75
≈ 293.8 cm
3 Answer(s): (a) 22 cm; (b) 293.8 cm
3