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Math Expert V
Joined: 02 Sep 2009
Posts: 59126
A cylinder of radius R and height H is reshaped. Which of the followin  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 41% (02:07) correct 59% (02:14) wrong based on 116 sessions

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A cylinder of radius R and height H is reshaped. Which of the following changes results in the cylinder of greatest volume?

A. a 20% decrease in H and a 50% increase in R.
B. a 500% increase in H and a 50% decrease in R.
C. a 300% increase in H and a 30% decrease in R.
D. a 70% decrease in H and a 100% increase in R.
E. a 100% increase in H and a 10% decrease in R.

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Re: A cylinder of radius R and height H is reshaped. Which of the followin  [#permalink]

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Bunuel wrote:
A cylinder of radius R and height H is reshaped. Which of the following changes results in the cylinder of greatest volume?

A. a 20% decrease in H and a 50% increase in R.
B. a 500% increase in H and a 50% decrease in R.
C. a 300% increase in H and a 30% decrease in R.
D. a 70% decrease in H and a 100% increase in R.
E. a 100% increase in H and a 10% decrease in R.

Initial Volume = (pi)R^2*H

Checking options

A. a 20% decrease in H and a 50% increase in R. i.e. Vol = (pi)(1.5R)^2*0.8H = 1.8* (pi)R^2*H
B. a 500% increase in H and a 50% decrease in R. i.e. Vol = (pi)(0.5R)^2*6H = 1.5* (pi)R^6*H
C. a 300% increase in H and a 30% decrease in R. i.e. Vol = (pi)(0.7R)^2*4H = 1.96* (pi)R^6*H
D. a 70% decrease in H and a 100% increase in R. i.e. Vol = (pi)(2R)^2*0.3H = 1.2* (pi)R^6*H
E. a 100% increase in H and a 10% decrease in R. i.e. Vol = (pi)(0.9R)^2*2H = 1.62* (pi)R^6*H

Maximum Increase is in Option C which is 96%

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A cylinder of radius R and height H is reshaped. Which of the followin  [#permalink]

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A cylinder of radius R and height H is reshaped. Which of the following changes results in the cylinder of greatest volume?

A. a 20% decrease in H and a 50% increase in R.
B. a 500% increase in H and a 50% decrease in R.
C. a 300% increase in H and a 30% decrease in R.
D. a 70% decrease in H and a 100% increase in R.
E. a 100% increase in H and a 10% decrease in R.

V= (pi) r^2 h
We will try to maximise (r^2)(h) here with special lookout on "r" as it doubles the number.

A. (1.5)^2 * (0.8) = 2.25 * 0.8 = 1.8
B. (0.5)^2 * (6) = 0.25 * 6 = 1.5
C. (0.7)^2 * (4) = 0.49 * 4 = 1.96
D. (2)^2 * (0.3) = 4 * 0.3 = 1.2
E. (0.9)^2 * (2) = 0.81 * 2 = 1.62

It should be C
Manager  Joined: 11 Jul 2016
Posts: 77
Re: A cylinder of radius R and height H is reshaped. Which of the followin  [#permalink]

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Volume of a cylinder = Pi. R^2.H

Check for options as per given Q.

A. (1.5)^2 * (0.8) = 2.25 * 0.8 = 1.8 (Since 20% decrease in H and a 50% increase in R.)
B. (0.5)^2 * (6) = 0.25 * 6 = 1.5 (Since 500% increase in H and a 50% decrease in R)
C. (0.7)^2 * (4) = 0.49 * 4 = 1.96 (Since 300% increase in H and a 30% decrease in R )
D. (2)^2 * (0.3) = 4 * 0.3 = 1.2 (Since 70% decrease in H and a 100% increase in R. )
E. (0.9)^2 * (2) = 0.81 * 2 = 1.62 (Since 100% increase in H and a 10% decrease in R. )

Maximum value is 1.96

Option C
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Re: A cylinder of radius R and height H is reshaped. Which of the followin  [#permalink]

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Bunuel wrote:
A cylinder of radius R and height H is reshaped. Which of the following changes results in the cylinder of greatest volume?

A. a 20% decrease in H and a 50% increase in R.
B. a 500% increase in H and a 50% decrease in R.
C. a 300% increase in H and a 30% decrease in R.
D. a 70% decrease in H and a 100% increase in R.
E. a 100% increase in H and a 10% decrease in R.

Let r=10 and h=10. Volume = Pi*r^2*h.

All we care about is r^2*h

Original Volume=10*10*10

A. 15*15*8
B. 60*5*5
C. 40*7*7
D. 3*20*20
E. 20*9*9

You know only contenders are B and C.

You can calculate and find out C is a bigger value.
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Director  P
Joined: 18 Dec 2017
Posts: 700
Location: United States (KS)
Re: A cylinder of radius R and height H is reshaped. Which of the followin  [#permalink]

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Note: 300% Increase means 30 more than 10. So the result will be 40. If the statement says 300% of 10 then it means 30 and not 40.
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You are missing on great learning if you don't know what this is: Project SC Butler Re: A cylinder of radius R and height H is reshaped. Which of the followin   [#permalink] 19 Oct 2019, 10:46
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