This figure is not drawn to scale. A rectangular glass container 80 cm by 56 cm by 45 cm has 2 compartments, Q and R, with a water height of 33 cm in Q and 20 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 115 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
= 28 x 33 x 56
= 51744 cm
3 Length of Compartment R
= 80 - 28
= 52 cm
Volume of the water in Compartment R
= 52 x 56 x 20
= 58240 cm
3 Total volume of water
= 51744 + 58240
= 109984 cm
3 Base area of the glass container
= 80 x 56
= 4480 cm
2 Height of water
= 109984 ÷ 4480
= 24.55 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment Q
= 33 - 24.55
= 8.45 cm
Drop in the volume of Compartment Q
= 56 x 28 x 8.45
= 13249.6 cm
3 Volume of water flowed from Q to R in 1 minute
= 13249.6 ÷ 72
≈ 184 cm
3 Answer(s): (a) 24.55 cm; (b) 184 cm
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