This figure is not drawn to scale. A rectangular glass container 72 cm by 59 cm by 47 cm has 2 compartments, D and E, with a water height of 39 cm in D and 12 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 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 D to E in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment D
= 26 x 39 x 59
= 59826 cm
3 Length of Compartment E
= 72 - 26
= 46 cm
Volume of the water in Compartment E
= 46 x 59 x 12
= 32568 cm
3 Total volume of water
= 59826 + 32568
= 92394 cm
3 Base area of the glass container
= 72 x 59
= 4248 cm
2 Height of water
= 92394 ÷ 4248
= 21.75 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment D
= 39 - 21.75
= 17.25 cm
Drop in the volume of Compartment D
= 59 x 26 x 17.25
= 26461.5 cm
3 Volume of water flowed from D to E in 1 minute
= 26461.5 ÷ 75
≈ 352.8 cm
3 Answer(s): (a) 21.75 cm; (b) 352.8 cm
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