This figure is not drawn to scale. A rectangular glass container 72 cm by 58 cm by 46 cm has 2 compartments, R and S, with a water height of 32 cm in R and 14 cm in S. A hole in the slider caused water to leak from R to S. 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 R to S in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment R
= 15 x 32 x 58
= 27840 cm
3 Length of Compartment S
= 72 - 15
= 57 cm
Volume of the water in Compartment S
= 57 x 58 x 14
= 46284 cm
3 Total volume of water
= 27840 + 46284
= 74124 cm
3 Base area of the glass container
= 72 x 58
= 4176 cm
2 Height of water
= 74124 ÷ 4176
= 17.75 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment R
= 32 - 17.75
= 14.25 cm
Drop in the volume of Compartment R
= 58 x 15 x 14.25
= 12397.5 cm
3 Volume of water flowed from R to S in 1 minute
= 12397.5 ÷ 105
≈ 118.1 cm
3 Answer(s): (a) 17.75 cm; (b) 118.1 cm
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