This figure is not drawn to scale. A rectangular glass tank 74 cm by 52 cm by 48 cm has 2 compartments, H and J, with a water height of 35 cm in H and 20 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 134 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
= 37 x 35 x 52
= 67340 cm
3 Length of Compartment J
= 74 - 37
= 37 cm
Volume of the water in Compartment J
= 37 x 52 x 20
= 38480 cm
3 Total volume of water
= 67340 + 38480
= 105820 cm
3 Base area of the glass tank
= 74 x 52
= 3848 cm
2 Height of water
= 105820 ÷ 3848
= 27.5 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment H
= 35 - 27.5
= 7.5 cm
Drop in the volume of Compartment H
= 52 x 37 x 7.5
= 14430 cm
3 Volume of water flowed from H to J in 1 minute
= 14430 ÷ 105
≈ 137.4 cm
3 Answer(s): (a) 27.5 cm; (b) 137.4 cm
3