This figure is not drawn to scale. A rectangular glass tank 85 cm by 57 cm by 42 cm has 2 compartments, J and K, with a water height of 37 cm in J and 20 cm in K. A hole in the slider caused water to leak from J to K. 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 J to K in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment J
= 19 x 37 x 57
= 40071 cm
3 Length of Compartment K
= 85 - 19
= 66 cm
Volume of the water in Compartment K
= 66 x 57 x 20
= 75240 cm
3 Total volume of water
= 40071 + 75240
= 115311 cm
3 Base area of the glass tank
= 85 x 57
= 4845 cm
2 Height of water
= 115311 ÷ 4845
= 23.8 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment J
= 37 - 23.8
= 13.2 cm
Drop in the volume of Compartment J
= 57 x 19 x 13.2
= 14295.6 cm
3 Volume of water flowed from J to K in 1 minute
= 14295.6 ÷ 90
≈ 158.8 cm
3 Answer(s): (a) 23.8 cm; (b) 158.8 cm
3