AustinKL wrote:
There are 2 circular cylinders X and Y, and both cylinders contain water inside. Cylinder X has \(5π\) square inches as the base area and 6 inches as the height of the water inside, and cylinder Y has \(10π\) square inches as the base area and 2 inches as the height of the water inside. If the height of the water becomes the same when the water drawn from cylinder X is poured into cylinder Y, what is the height of water in these cylinders, in inches?
A. 2.5
B. 3
C. \(\frac{10}{3}\)
D. 4
E. 4.5
First let’s determine the volume of water in each of the two cylinders before water from one is poured into the other. Recall that the volume of a cylinder is V = Bh, in which B is the circular base area and h is the height of the cylinder. Thus we have:
Water in cylinder X: Volume = 5? x 6 = 30? in^3
Water in cylinder Y: Volume = 10? x 2 = 20? in^3
Now we can let w be the amount of water that should be poured from cylinder X to cylinder Y so that the water in both cylinders will be the same height. Notice that if V = Bh, then h = V/B.
Thus we have:
(30? - w)/5? = (20? + w)/10?
5?(20? + w) = 10?(30? - w)
100?^2 + 5w? = 300?^2 - 10w?
15w? = 200?^2
3w = 40?
w = 40?/3
Since w = 40?/3, the height of water in each cylinder is:
(30? - 40?/3)/5?
(90? - 40?)/15?
50?/15? = 10/3
Answer: C
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