This figure is not drawn to scale. A rectangular glass tank 75 cm by 60 cm by 47 cm has 2 compartments, J and K, with a water height of 38 cm in J and 13 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
= 15 x 38 x 60
= 34200 cm
3 Length of Compartment K
= 75 - 15
= 60 cm
Volume of the water in Compartment K
= 60 x 60 x 13
= 46800 cm
3 Total volume of water
= 34200 + 46800
= 81000 cm
3 Base area of the glass tank
= 75 x 60
= 4500 cm
2 Height of water
= 81000 ÷ 4500
= 18 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment J
= 38 - 18
= 20 cm
Drop in the volume of Compartment J
= 60 x 15 x 20
= 18000 cm
3 Volume of water flowed from J to K in 1 minute
= 18000 ÷ 90
≈ 200.0 cm
3 Answer(s): (a) 18 cm; (b) 200.0 cm
3