This figure is not drawn to scale. A rectangular glass tank 75 cm by 53 cm by 49 cm has 2 compartments, J and K, with a water height of 34 cm in J and 16 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
= 35 x 34 x 53
= 63070 cm
3 Length of Compartment K
= 75 - 35
= 40 cm
Volume of the water in Compartment K
= 40 x 53 x 16
= 33920 cm
3 Total volume of water
= 63070 + 33920
= 96990 cm
3 Base area of the glass tank
= 75 x 53
= 3975 cm
2 Height of water
= 96990 ÷ 3975
= 24.4 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment J
= 34 - 24.4
= 9.6 cm
Drop in the volume of Compartment J
= 53 x 35 x 9.6
= 17808 cm
3 Volume of water flowed from J to K in 1 minute
= 17808 ÷ 90
≈ 197.9 cm
3 Answer(s): (a) 24.4 cm; (b) 197.9 cm
3