This figure is not drawn to scale. A rectangular glass tank 88 cm by 59 cm by 41 cm has 2 compartments, H and J, with a water height of 32 cm in H and 18 cm in J. A hole in the slider caused water to leak from H to J. 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 H to J in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment H
= 33 x 32 x 59
= 62304 cm
3 Length of Compartment J
= 88 - 33
= 55 cm
Volume of the water in Compartment J
= 55 x 59 x 18
= 58410 cm
3 Total volume of water
= 62304 + 58410
= 120714 cm
3 Base area of the glass tank
= 88 x 59
= 5192 cm
2 Height of water
= 120714 ÷ 5192
= 23.25 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment H
= 32 - 23.25
= 8.75 cm
Drop in the volume of Compartment H
= 59 x 33 x 8.75
= 17036.25 cm
3 Volume of water flowed from H to J in 1 minute
= 17036.25 ÷ 90
≈ 189.3 cm
3 Answer(s): (a) 23.25 cm; (b) 189.3 cm
3