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# A certain right circular cylinder has a radius of 5 inches. A certain

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Math Expert
Joined: 02 Sep 2009
Posts: 54370
A certain right circular cylinder has a radius of 5 inches. A certain  [#permalink]

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07 Jul 2017, 00:41
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93% (01:40) correct 8% (02:41) wrong based on 52 sessions

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A certain right circular cylinder has a radius of 5 inches. A certain quantity of liquid fills this cylinder to a height of 9 inches. When all of this liquid is poured into a second right circular cylinder, the liquid fills the second cylinder to a height of 4 inches. What is the radius of the second cylinder, in inches?

(A) 6.0
(B) 6.5
(C) 7.0
(D) 7.5
(E) 8.0

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A certain right circular cylinder has a radius of 5 inches. A certain  [#permalink]

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07 Jul 2017, 02:58
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Bunuel wrote:
A certain right circular cylinder has a radius of 5 inches. A certain quantity of liquid fills this cylinder to a height of 9 inches. When all of this liquid is poured into a second right circular cylinder, the liquid fills the second cylinder to a height of 4 inches. What is the radius of the second cylinder, in inches?

(A) 6.0
(B) 6.5
(C) 7.0
(D) 7.5
(E) 8.0

It should be D.

Lets say first cylinder is has a radius R1 and height h1 while the second cylinder has a height R2 and height h2. Since they both fill the same volume, we can equate their filled areas as equivalent cylinders.

$$πR2^2h2 = πR1^2h1$$

pi is cancelled on each side.

$$R2^2 * 4 = 5^2 * 9$$
$$R2^2 * 4 = 225$$

$$R2^2 = 225/4$$

$$R2 = 15/2$$

which is 7.5 or D
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Re: A certain right circular cylinder has a radius of 5 inches. A certain  [#permalink]

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07 Jul 2017, 04:20
Bunuel wrote:
A certain right circular cylinder has a radius of 5 inches. A certain quantity of liquid fills this cylinder to a height of 9 inches. When all of this liquid is poured into a second right circular cylinder, the liquid fills the second cylinder to a height of 4 inches. What is the radius of the second cylinder, in inches?

(A) 6.0
(B) 6.5
(C) 7.0
(D) 7.5
(E) 8.0

Volume of Liquid in both cylinders is same hence

Volume of first cylinder with height 9 = Volume of first cylinder with height 4

(Pi)r^2*9 = (Pi)r^2*4
5^2*9 = r^2*4
(5^2*9)/4 = r^2
i/.e. r = 15/2

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Re: A certain right circular cylinder has a radius of 5 inches. A certain  [#permalink]

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12 Jul 2017, 16:35
1
Bunuel wrote:
A certain right circular cylinder has a radius of 5 inches. A certain quantity of liquid fills this cylinder to a height of 9 inches. When all of this liquid is poured into a second right circular cylinder, the liquid fills the second cylinder to a height of 4 inches. What is the radius of the second cylinder, in inches?

(A) 6.0
(B) 6.5
(C) 7.0
(D) 7.5
(E) 8.0

Let’s find the volume of the liquid in the first cylinder:

V = πr^2 * h = π(5)^2 * 9 = 225π cubic inches

Now we can let x = radius of the second cylinder and solve for x by setting the volume of the liquid in the second cylinder equal to 225π:

πx^2 * 4 = 225π

x^2 * 4 = 225

x^2 = 225/4

x = √(225/4)

x = 15/2

x = 7.5

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Re: A certain right circular cylinder has a radius of 5 inches. A certain   [#permalink] 12 Jul 2017, 16:35
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