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A soda can, in the shape of a right circular cylinder, is

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A soda can, in the shape of a right circular cylinder, is  [#permalink]

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New post 28 May 2012, 02:50
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A soda can, in the shape of a right circular cylinder, is 3/4 full of soda. If the volume of soda in the can is 72π cubic inches and the diameter of the can is 8 inches, then what is the height, in inches, of the can?

A. 1.5
B. 3
C. 4
D. 4.5
E. 6
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Re: A soda can, in the shape of a right circular cylinder, is  [#permalink]

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New post 28 May 2012, 02:56
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macjas wrote:
A soda can, in the shape of a right circular cylinder, is 3/4 full of soda. If the volume of soda in the can is 72π cubic inches and the diameter of the can is 8 inches, then what is the height, in inches, of the can?

A. 1.5
B. 3
C. 4
D. 4.5
E. 6


Since the volume of soda in the can is \(72\pi\) and the can is 3/4 full of soda then the volume of the can is \(\frac{3}{4}*can=72\pi\) --> \(can=96\pi\).

The volume of a cylinder is \(\pi{r^2}h\) --> \(\pi{4^2}h=96\pi\) --> \(h=6\).

Answer: E.
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Re: A soda can, in the shape of a right circular cylinder, is  [#permalink]

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New post 19 Jul 2018, 12:33
macjas wrote:
A soda can, in the shape of a right circular cylinder, is 3/4 full of soda. If the volume of soda in the can is 72π cubic inches and the diameter of the can is 8 inches, then what is the height, in inches, of the can?

A. 1.5
B. 3
C. 4
D. 4.5
E. 6


First, let V = the volume of the entire soda can. Since the volume of soda is 72π cubic inches and that represents 3/4 of the volume of the entire soda can, we see that:

(3/4)V = 72π

3V = 288π

V = 96π

Now, using the volume formula of a cylinder, we can solve the height of the can:

V = π r^2 h

96π = π (4)^2 h

96π = 16π h

6 = h

Answer: E
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Re: A soda can, in the shape of a right circular cylinder, is  [#permalink]

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New post 24 Jul 2018, 00:48
Alternatively, one can find the height of the can with the water, which is 9/2 then create a ratio. If 9/2 / 75% than H/100. So the H (height) is 6.
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Re: A soda can, in the shape of a right circular cylinder, is &nbs [#permalink] 24 Jul 2018, 00:48
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