This figure is not drawn to scale. A rectangular glass container 75 cm by 53 cm by 47 cm has 2 compartments, Q and R, with a water height of 38 cm in Q and 12 cm in R. A hole in the slider caused water to leak from Q to R. 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 Q to R in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Q
= 24 x 38 x 53
= 48336 cm
3 Length of Compartment R
= 75 - 24
= 51 cm
Volume of the water in Compartment R
= 51 x 53 x 12
= 32436 cm
3 Total volume of water
= 48336 + 32436
= 80772 cm
3 Base area of the glass container
= 75 x 53
= 3975 cm
2 Height of water
= 80772 ÷ 3975
= 20.32 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment Q
= 38 - 20.32
= 17.68 cm
Drop in the volume of Compartment Q
= 53 x 24 x 17.68
= 22488.96 cm
3 Volume of water flowed from Q to R in 1 minute
= 22488.96 ÷ 75
≈ 299.9 cm
3 Answer(s): (a) 20.32 cm; (b) 299.9 cm
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