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# A cylinder whose volume is 900 cubic inches is reshaped such that its

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A cylinder whose volume is 900 cubic inches is reshaped such that its  [#permalink]

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02 Jun 2015, 11:14
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Difficulty:

55% (hard)

Question Stats:

55% (01:31) correct 45% (01:52) wrong based on 107 sessions

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A cylinder whose volume is 900 cubic inches is reshaped such that its volume remains unchanged. If its diameter is reduced by 50%, then its height must be increased by:

A. 50%
B. 100%
C. 200%
D. 300%
E. 400%

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A cylinder whose volume is 900 cubic inches is reshaped such that its  [#permalink]

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03 Oct 2015, 05:27
reto wrote:
A cylinder whose volume is 900 cubic inches is reshaped such that its volume remains unchanged. If its diameter is reduced by 50%, then its height must be increased by:

A. 50%
B. 100%
C. 200%
D. 300%
E. 400%

If volume remains same, then $$\pi{r}^{2}{h}$$ remains same. Hence, if radius is halved then height must become 4 times for the quantity $${r}^{2}{h}$$ to remain constant. Hence, height must increase by 300%.
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A cylinder whose volume is 900 cubic inches is reshaped such that its  [#permalink]

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Updated on: 04 Oct 2015, 13:04
The volume of the cylinder doesn't matter. We just have to set up the equations.
We are trying to find $$\frac{h(new)}{h(old)}-1$$

$$\pi r^2*h(old) =\pi(\frac{r}{2})^2*h(new)$$

$$\frac{4}{\pi r^2}*\pi r^2=\frac{h(new)}{h(old)} = 4$$

$$\frac{h(new)}{h(old)}-1= 4 - 1 = 3$$

This translates into a 300% increase.

Originally posted by Marchewski on 04 Oct 2015, 11:56.
Last edited by Marchewski on 04 Oct 2015, 13:04, edited 2 times in total.
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Re: A cylinder whose volume is 900 cubic inches is reshaped such that its  [#permalink]

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04 Oct 2015, 12:50
reto wrote:
A cylinder whose volume is 900 cubic inches is reshaped such that its volume remains unchanged. If its diameter is reduced by 50%, then its height must be increased by:

A. 50%
B. 100%
C. 200%
D. 300%
E. 400%

Step 1: 900 = πr^2*h

Step 2: recognize that Diameter = 2*radius, and radius = Diameter /2. If Diameter is reduced by 50%, then new Diameter is D/2 = 2r/2 = r. And since radius is half of the diameter, the new radius is D/2/2 = r/2.

Step 3: plug new radius in the formula --> 900 = π(r/2)^2*h = π(r^2/4)*h

Step 4: since the RHS of the equation is now multiplied by 1/4, h must be 4h to keep the equation unchanged. 4h is a 300% increase from h. Not 400% increase
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Re: A cylinder whose volume is 900 cubic inches is reshaped such that its  [#permalink]

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12 Nov 2015, 09:50
why is not 400%?
can you make the calculation? tksss
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Re: A cylinder whose volume is 900 cubic inches is reshaped such that its  [#permalink]

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12 Nov 2015, 22:48
gabriela2015 wrote:
why is not 400%?
can you make the calculation? tksss

5*(1+300%) = 5*(100%+300%)=5*(400%)=5*4

Therefore 5*4 -> 4 times is 300% increase of 5 not 400% increase.
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Re: A cylinder whose volume is 900 cubic inches is reshaped such that its  [#permalink]

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14 Mar 2018, 00:02
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Re: A cylinder whose volume is 900 cubic inches is reshaped such that its   [#permalink] 14 Mar 2018, 00:02
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