This figure is not drawn to scale. A rectangular glass container 90 cm by 53 cm by 49 cm has 2 compartments, D and E, with a water height of 38 cm in D and 13 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
= 36 x 38 x 53
= 72504 cm
3 Length of Compartment E
= 90 - 36
= 54 cm
Volume of the water in Compartment E
= 54 x 53 x 13
= 37206 cm
3 Total volume of water
= 72504 + 37206
= 109710 cm
3 Base area of the glass container
= 90 x 53
= 4770 cm
2 Height of water
= 109710 ÷ 4770
= 23 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment D
= 38 - 23
= 15 cm
Drop in the volume of Compartment D
= 53 x 36 x 15
= 28620 cm
3 Volume of water flowed from D to E in 1 minute
= 28620 ÷ 105
≈ 272.6 cm
3 Answer(s): (a) 23 cm; (b) 272.6 cm
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