This figure is not drawn to scale. A rectangular glass container 84 cm by 55 cm by 45 cm has 2 compartments, D and E, with a water height of 40 cm in D and 19 cm in E. A hole in the slider caused water to leak from D to E. 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 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 D to E in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment D
= 24 x 40 x 55
= 52800 cm
3 Length of Compartment E
= 84 - 24
= 60 cm
Volume of the water in Compartment E
= 60 x 55 x 19
= 62700 cm
3 Total volume of water
= 52800 + 62700
= 115500 cm
3 Base area of the glass container
= 84 x 55
= 4620 cm
2 Height of water
= 115500 ÷ 4620
= 25 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment D
= 40 - 25
= 15 cm
Drop in the volume of Compartment D
= 55 x 24 x 15
= 19800 cm
3 Volume of water flowed from D to E in 1 minute
= 19800 ÷ 105
≈ 188.6 cm
3 Answer(s): (a) 25 cm; (b) 188.6 cm
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