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If the ratio of the volumes of two right circular cylinders

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by BTGmoderatorDC » Tue Jul 24, 2018 5:15 pm

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B

C

D

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Difficulty—

If the ratio of the volumes of two right circular cylinders is given by 64/9, what is the ratio of their radii? (Both the cylinders have the same height)

(A) 4/3
(B) 8/3
(C) 16/9
(D) 4/1
(E) 16/3
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by [email protected] » Tue Jul 24, 2018 9:10 pm
Hi All,

We're told that two right circular cylinders have the SAME height and the ratio of their volumes is given by 64/9. We're asked for the ratio of their radii.

Volume of a cylinder = (pi)(R^2)(H)

Since the cylinders have the SAME height, that value (whatever it is) doesn't impact the ratio of the two volumes. Thus, the ratio is completely depended on the radius of each cylinder (specifically, radius-squared). Thus, we're looking for the square-roots of 64 and 9. That would be 8 and 3, respectively.

We can prove that this is the correct answer with the following example:
1st cylinder: radius = 8, height = 1, Volume = (pi)(64)(1) = 64pi
2nd cylinder: radius = 3, height = 1, Volume = (pi)(9)(1) = 9pi
64pi:9pi = 64/9

Final Answer: B

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by Jeff@TargetTestPrep » Thu Jul 26, 2018 3:26 pm
BTGmoderatorDC wrote:If the ratio of the volumes of two right circular cylinders is given by 64/9, what is the ratio of their radii? (Both the cylinders have the same height)

(A) 4/3
(B) 8/3
(C) 16/9
(D) 4/1
(E) 16/3
Let the larger radius = R and the smaller radius = r; thus, we have:

(Ï€ R^2 h)/(Ï€ r^2 h) = 64/9

R^2/r^2 = 64/9

Taking the square root of both sides, we have:

R/r = 8/3

Answer: B

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