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If a right circular cylinder’s radius is halved and its heig
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19 Sep 2018, 17:52
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
(A) 50% decrease
(B) 0%
(C) 25% increase
(D) 50% increase
(E) 100% increase
Re: If a right circular cylinder’s radius is halved and its heig
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15 Apr 2020, 06:15
15 Apr 2020, 06:15
1
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
(A) 50% decrease
(B) 0%
(C) 25% increase
(D) 50% increase
(E) 100% increase
Volume of a circular cylinder = \(\pi\) * \({radius}^2\) * height
now, when the radius is reduced by 2 and height doubled, volume = \(\pi * {\frac{R}{2}}^2 * 2H\)= \(\frac{{\pi * {R}^2 * H}}{2} \), which is decreased by 50%
*****We can use some nice nos.
Let Radius = 4
Height = 2
Volume =\( \pi*4^2 * 2 = 32\pi\)
Radius is halved and height doubled, volume =\( \pi*2^2 * 4 = 16\pi\) , i.e volume decreased by 50%
Re: If a right circular cylinder’s radius is halved and its heig
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11 May 2020, 03:39
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.
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.
