This figure is not drawn to scale. A rectangular glass container 84 cm by 54 cm by 46 cm has 2 compartments, K and L, with a water height of 33 cm in K and 12 cm in L. A hole in the slider caused water to leak from K to L. 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 K to L in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment K
= 33 x 33 x 54
= 58806 cm
3 Length of Compartment L
= 84 - 33
= 51 cm
Volume of the water in Compartment L
= 51 x 54 x 12
= 33048 cm
3 Total volume of water
= 58806 + 33048
= 91854 cm
3 Base area of the glass container
= 84 x 54
= 4536 cm
2 Height of water
= 91854 ÷ 4536
= 20.25 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment K
= 33 - 20.25
= 12.75 cm
Drop in the volume of Compartment K
= 54 x 33 x 12.75
= 22720.5 cm
3 Volume of water flowed from K to L in 1 minute
= 22720.5 ÷ 72
≈ 315.6 cm
3 Answer(s): (a) 20.25 cm; (b) 315.6 cm
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