This figure is not drawn to scale. A rectangular glass container 85 cm by 51 cm by 43 cm has 2 compartments, D and E, with a water height of 36 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 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
= 12 x 36 x 51
= 22032 cm
3 Length of Compartment E
= 85 - 12
= 73 cm
Volume of the water in Compartment E
= 73 x 51 x 19
= 70737 cm
3 Total volume of water
= 22032 + 70737
= 92769 cm
3 Base area of the glass container
= 85 x 51
= 4335 cm
2 Height of water
= 92769 ÷ 4335
= 21.4 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment D
= 36 - 21.4
= 14.6 cm
Drop in the volume of Compartment D
= 51 x 12 x 14.6
= 8935.2 cm
3 Volume of water flowed from D to E in 1 minute
= 8935.2 ÷ 75
≈ 119.1 cm
3 Answer(s): (a) 21.4 cm; (b) 119.1 cm
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