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If the ratio of the volumes of two right circular cylinders is given

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If the ratio of the volumes of two right circular cylinders is given [#permalink]

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New post 07 Jul 2017, 00:55
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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
[Reveal] Spoiler: OA

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If the ratio of the volumes of two right circular cylinders is given [#permalink]

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New post 07 Jul 2017, 01:48
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Bunuel 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


It should be B.

Lets say larger of the two cylinders has radius R and height H. Smaller has the radius r and height h. We know that volume of cylinder is \(πR^2h\)

\(πR^2H / πr^2h\) = \(64/9\)

Since height is same, we can cross π and h

\(R^2/r^2\) = \(64/9\)

Taking square root of both sides and it comes out to be ratio of radii. 8/3 or B
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If the ratio of the volumes of two right circular cylinders is given [#permalink]

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New post 07 Jul 2017, 05:46
Bunuel 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 Volume of one cylinder be \(=\) \(\pi\)\(R^2h\)

Let Volume of second cylinder be \(=\) \(\pi\)\(r^2h\)

Given Both cylinders have same height.

Ratio of Volumes \(=> \frac{\pi(R^2)h}{\pi(r^2)h} = \frac{64}{9}\)

\(\frac{R^2}{r^2} = \frac{64}{9}\)

\(\sqrt{\frac{R^2}{r^2}} = \sqrt{\frac{64}{9}}\)

Ratio of Radii \(=> \frac{R}{r} = \frac{8}{3}\)

Answer (B)...

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Re: If the ratio of the volumes of two right circular cylinders is given [#permalink]

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New post 05 Jan 2018, 19:54
Volume of right circular cylinder V = pi*r^2*l
V1 = pi*r1^2*l1
V2 = pi*r2^2*l2

Ratio of volume: V1/V2 =64/9

Since l= is constant => l1=l2
V1/V2 =r1*r1/r2*r2 = 64/9
=> r1/r2 =8 /3

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Re: If the ratio of the volumes of two right circular cylinders is given   [#permalink] 05 Jan 2018, 19:54
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