This figure is not drawn to scale. A rectangular glass container 75 cm by 54 cm by 47 cm has 2 compartments, R and S, with a water height of 40 cm in R and 17 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
= 33 x 40 x 54
= 71280 cm
3 Length of Compartment S
= 75 - 33
= 42 cm
Volume of the water in Compartment S
= 42 x 54 x 17
= 38556 cm
3 Total volume of water
= 71280 + 38556
= 109836 cm
3 Base area of the glass container
= 75 x 54
= 4050 cm
2 Height of water
= 109836 ÷ 4050
= 27.12 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment R
= 40 - 27.12
= 12.88 cm
Drop in the volume of Compartment R
= 54 x 33 x 12.88
= 22952.16 cm
3 Volume of water flowed from R to S in 1 minute
= 22952.16 ÷ 105
≈ 218.6 cm
3 Answer(s): (a) 27.12 cm; (b) 218.6 cm
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