This figure is not drawn to scale. A rectangular glass tank 75 cm by 52 cm by 43 cm has 2 compartments, J and K, with a water height of 31 cm in J and 11 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
= 21 x 31 x 52
= 33852 cm
3 Length of Compartment K
= 75 - 21
= 54 cm
Volume of the water in Compartment K
= 54 x 52 x 11
= 30888 cm
3 Total volume of water
= 33852 + 30888
= 64740 cm
3 Base area of the glass tank
= 75 x 52
= 3900 cm
2 Height of water
= 64740 ÷ 3900
= 16.6 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment J
= 31 - 16.6
= 14.4 cm
Drop in the volume of Compartment J
= 52 x 21 x 14.4
= 15724.8 cm
3 Volume of water flowed from J to K in 1 minute
= 15724.8 ÷ 90
≈ 174.7 cm
3 Answer(s): (a) 16.6 cm; (b) 174.7 cm
3