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Math Expert V
Joined: 02 Sep 2009
Posts: 59089
If the ratio of the volumes of two right circular cylinders is given  [#permalink]

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Difficulty:   5% (low)

Question Stats: 89% (00:53) correct 11% (01:35) wrong based on 141 sessions

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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

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Manager  P
Joined: 14 Oct 2015
Posts: 243
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If the ratio of the volumes of two right circular cylinders is given  [#permalink]

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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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Director  V
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Concentration: Technology, Strategy
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If the ratio of the volumes of two right circular cylinders is given  [#permalink]

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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

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 $$=> \frac{R}{r} = \frac{8}{3}$$

Manager  B
Joined: 23 Oct 2017
Posts: 60
Re: If the ratio of the volumes of two right circular cylinders is given  [#permalink]

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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
Target Test Prep Representative G
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Posts: 2812
Re: If the ratio of the volumes of two right circular cylinders is given  [#permalink]

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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

Let the larger radius = R and the smaller radius = r; thus, we have:

(π R^2 h)/(π r^2 h) = 64/9

R^2/r^2 = 64/9

Taking the square root of both sides, we have:

R/r = 8/3

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

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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

Letting r1 and r2 = the radii of the two cylinders, respectively, we can create the equation:

(π*r1^2*h)/(π*r2^2*h) = 64/9

r1^2/r2^2 = 64/9

Taking the square root of both sides, we have:

r1/r2 = 8/3

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# Scott Woodbury-Stewart

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If the ratio of the volumes of two right circular cylinders is given   [#permalink] 11 Oct 2019, 15:46
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