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

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Math Expert
Joined: 02 Sep 2009
Posts: 46195
If the ratio of the volumes of two right circular cylinders is given [#permalink]

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07 Jul 2017, 01:55
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Difficulty:

5% (low)

Question Stats:

91% (00:37) correct 9% (00:50) wrong based on 104 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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Joined: 14 Oct 2015
Posts: 245
GPA: 3.57
If the ratio of the volumes of two right circular cylinders is given [#permalink]

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07 Jul 2017, 02:48
1
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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07 Jul 2017, 06:46
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 $$=> \frac{R}{r} = \frac{8}{3}$$

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Joined: 23 Oct 2017
Posts: 64
Re: If the ratio of the volumes of two right circular cylinders is given [#permalink]

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05 Jan 2018, 20:54
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
Re: If the ratio of the volumes of two right circular cylinders is given   [#permalink] 05 Jan 2018, 20:54
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