This figure is not drawn to scale. A rectangular glass container 75 cm by 57 cm by 40 cm has 2 compartments, R and S, with a water height of 40 cm in R and 13 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 115 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
= 16 x 40 x 57
= 36480 cm
3 Length of Compartment S
= 75 - 16
= 59 cm
Volume of the water in Compartment S
= 59 x 57 x 13
= 43719 cm
3 Total volume of water
= 36480 + 43719
= 80199 cm
3 Base area of the glass container
= 75 x 57
= 4275 cm
2 Height of water
= 80199 ÷ 4275
= 18.76 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment R
= 40 - 18.76
= 21.24 cm
Drop in the volume of Compartment R
= 57 x 16 x 21.24
= 19370.88 cm
3 Volume of water flowed from R to S in 1 minute
= 19370.88 ÷ 72
≈ 269 cm
3 Answer(s): (a) 18.76 cm; (b) 269 cm
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