This figure is not drawn to scale. A rectangular glass container 70 cm by 59 cm by 43 cm has 2 compartments, W and X, with a water height of 35 cm in W and 14 cm in X. A hole in the slider caused water to leak from W to X. It was found that the water level in both compartments became the same after some time.
- What is the height of water in the container 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 W to X in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment W
= 40 x 35 x 59
= 82600 cm
3 Length of Compartment X
= 70 - 40
= 30 cm
Volume of the water in Compartment X
= 30 x 59 x 14
= 24780 cm
3 Total volume of water
= 82600 + 24780
= 107380 cm
3 Base area of the glass container
= 70 x 59
= 4130 cm
2 Height of water
= 107380 ÷ 4130
= 26 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment W
= 35 - 26
= 9 cm
Drop in the volume of Compartment W
= 59 x 40 x 9
= 21240 cm
3 Volume of water flowed from W to X in 1 minute
= 21240 ÷ 90
≈ 236.0 cm
3 Answer(s): (a) 26 cm; (b) 236.0 cm
3