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If a right circular cylinder’s radius is halved and its heig

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sandy
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If a right circular cylinder’s radius is halved and its heig [#permalink] New post   19 Sep 2018, 17:52
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If a right circular cylinder’s radius is halved and its height doubled, by what percent will the volume increase or decrease?

(A) 50% decrease
(B) 0%
(C) 25% increase
(D) 50% increase
(E) 100% increase
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A
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Re: If a right circular cylinder’s radius is halved and its heig [#permalink] New post   15 Apr 2020, 06:15
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sandy wrote:
If a right circular cylinder’s radius is halved and its height doubled, by what percent will the volume increase or decrease?

(A) 50% decrease
(B) 0%
(C) 25% increase
(D) 50% increase
(E) 100% increase


Volume of a circular cylinder = π * radius2 * height

now, when the radius is reduced by 2 and height doubled, volume = π∗R22∗2H= π∗R2∗H2, which is decreased by 50%

*****We can use some nice nos.

Let Radius = 4

Height = 2

Volume =π∗42∗2=32π

Radius is halved and height doubled, volume =π∗22∗4=16π , i.e volume decreased by 50%
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Re: If a right circular cylinder’s radius is halved and its heig [#permalink] New post   11 May 2020, 03:39
Using Numbers

let r = 4 and h = 2

Volume = pi.16.2 = 32.pi

Now, r = 2 and h = 4, since radius is halved and height is doubled. We get,

New Volume = pi.4.4 = 16.pi

We see that the new volume is half that of the old volume so the volume decreases by 50%, Answer is A.

Using Formulas

Old Volume = pi.r.r.h

New Volume = pi.(r/2).(r/2).2h

= (pi.r.r.2.h)/4

= (pi.r.r.h)/2

New Volume is half that of the Old Volume, therefore there is a 50% decrease in volume, Answer is A.
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Re: If a right circular cylinder’s radius is halved and its heig [#permalink] New post   08 Sep 2021, 08:19
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Re: If a right circular cylinder’s radius is halved and its heig [#permalink]
08 Sep 2021, 08:19
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