This figure is not drawn to scale. A rectangular glass container 77 cm by 51 cm by 46 cm has 2 compartments, W and X, with a water height of 34 cm in W and 13 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 114 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
= 33 x 34 x 51
= 57222 cm
3 Length of Compartment X
= 77 - 33
= 44 cm
Volume of the water in Compartment X
= 44 x 51 x 13
= 29172 cm
3 Total volume of water
= 57222 + 29172
= 86394 cm
3 Base area of the glass container
= 77 x 51
= 3927 cm
2 Height of water
= 86394 ÷ 3927
= 22 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment W
= 34 - 22
= 12 cm
Drop in the volume of Compartment W
= 51 x 33 x 12
= 20196 cm
3 Volume of water flowed from W to X in 1 minute
= 20196 ÷ 75
≈ 269.3 cm
3 Answer(s): (a) 22 cm; (b) 269.3 cm
3