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

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Math Expert
Joined: 02 Sep 2009
Posts: 60555
A cylinder whose volume is 900 cubic inches is reshaped such that its  [#permalink]

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07 Nov 2019, 01:40
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Difficulty:

55% (hard)

Question Stats:

62% (01:32) correct 38% (01:43) wrong based on 63 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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Intern
Joined: 10 Oct 2019
Posts: 11
GMAT 1: 400 Q35 V12
Re: A cylinder whose volume is 900 cubic inches is reshaped such that its  [#permalink]

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07 Nov 2019, 03:22
1
and: D 300%
--> Volume=πr2·H

--> πr2·H = 900

Plug in a nice r such as r = 10 (so that r2=100). The resulting H is = 9/π.

Now, If r is reduced by 50%, it is now 5.

Plug in the new r=5, and find the new H.

--> π·52·H = 900

--> H = 900/(25π) = 36/π

The original H was 9/π, so H is multiplied times 4. However, this only represents a 300% increase from the original height.
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Re: A cylinder whose volume is 900 cubic inches is reshaped such that its  [#permalink]

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07 Nov 2019, 09:09
Bunuel 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%

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given
pi*r^2*h = 900
dia is 50% reduced ; r= d/4
pi*r^2/4*h=900
pi*r^2*h=3600
so change in height = 3600-900/900 ; 300%
IMO D
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Joined: 17 May 2019
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Re: A cylinder whose volume is 900 cubic inches is reshaped such that its  [#permalink]

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07 Nov 2019, 19:13
Given- pi* r^2*h =900
as r=d/2
so pi*(d/2)^2*h=900
pi*d^2*h=3600 ---1

the diameter is reduced to 50%
pi*(d/2)^2 *h =3600
pi*d^2 *h=14400 --2

we need to find the % increase in height :
(14400-3600/3600) *100
on solving 300%
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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 2019, 20:22
Bunuel 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%

Are You Up For the Challenge: 700 Level Questions

We can let h = the original height of the cylinder and H = the new height of the cylinder.

We can let the original diameter = 20, so we have:

900 = ?(10)^2 * h

900 = 100?h

9/? = h

If the diameter is reduced by 1/2, the radius is also reduced by 1/2, so we have:

900 = ?(5)^2 * H

900 = 25?H

36/? = H

We see that the new height is 4 times the old height; therefore, the height must be increased by 300%.

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Re: A cylinder whose volume is 900 cubic inches is reshaped such that its   [#permalink] 12 Nov 2019, 20:22
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