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For a certain cylinder, the diameter equals the height. [#permalink]

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24 Mar 2014, 15:20

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For a certain cylinder, the diameter equals the height. If every length in this cylinder is decreased by 60%, then to the nearest integer, by what percent does the volume decrease?

(A) 22%

(B) 40%

(C) 60%

(D) 84%

(E) 94 %

This is how I am doing it but getting the incorrect answer. Can someone please help?

Case 1: Assume diameter = 10 then radius = 5 and height will be 10

For a certain cylinder, the diameter equals the height. [#permalink]

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24 Mar 2014, 19:00

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This post received KUDOS

enigma123 wrote:

For a certain cylinder, the diameter equals the height. If every length in this cylinder is decreased by 60%, then to the nearest integer, by what percent does the volume decrease?

(A) 22%

(B) 40%

(C) 60%

(D) 84%

(E) 94 %

This is how I am doing it but getting the incorrect answer. Can someone please help?

Case 1: Assume diameter = 10 then radius = 5 and height will be 10

For a certain cylinder, the diameter equals the height. If every length in this cylinder is decreased by 60%, then to the nearest integer, by what percent does the volume decrease?

New volume = pi*25*4 = 100pi-----------------------------------------------------(2)

Volume decrease in percent = Old - new / old *100

250 pi - 100 pi/250pi * 100 = 60 % which is not correct.

The area of the cylinder is \(\pi{r^2}h\). Since given that the diameter equals the height, then 2r=h and the area becomes \(2\pi{r^3}\).

Now, if we decrease r by 60% it becomes 0.4r and thus the new volume becomes \(0.4^3*(2\pi{r^3})=0.064*(2\pi{r^3})\). Therefore the volume decreased by approximately 1-0.06=0.94=94%.

Re: For a certain cylinder, the diameter equals the height. [#permalink]

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18 Jan 2015, 05:54

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This post received KUDOS

enigma123 wrote:

For a certain cylinder, the diameter equals the height. If every length in this cylinder is decreased by 60%, then to the nearest integer, by what percent does the volume decrease?

(A) 22%

(B) 40%

(C) 60%

(D) 84%

(E) 94 %

This is how I am doing it but getting the incorrect answer. Can someone please help?

Case 1: Assume diameter = 10 then radius = 5 and height will be 10

New volume = pi*25*4 = 100pi-----------------------------------------------------(2)

Volume decrease in percent = Old - new / old *100

250 pi - 100 pi/250pi * 100 = 60 % which is not correct.

Given, all the lengths of the cylinder are reduced by 60% Hence all the lengths are now 40% of actual!

Original Volume (V)= (pi)(r*r)(h) New Volume (V1) = (pi)(0.4r*0.4r)(0.4h) = (0.064)(pi)(r*r)(h) = 0.064V Thus new Volume is 6.4% of original Volume This implies the volume has reduced by 93.6% which after rounding off becomes 94%

Since this question does not include any specific dimensions for the cylinder, we can TEST VALUES.

We're told that the Diameter = Height

IF.... Diameter = Height = 10

Volume = pi(R^2)(H) V = pi(5^2)(10) V = 250pi

We're then told that both measurements are reduced by 60%...

Diameter = Height = 4

New Volume = pi(2^2)(4) New Volume = 16pi

The question asks us for the approximate percentage change in the Volume, so we need the Percentage Change Formula:

(New - Old)/Old = (16 - 250)/250 = -234/250

From here, we don't really need to calculate; we can use the answer choices to our advantage and do "comparison" math instead...

10% of 250 = 25 234 is "16 away" from 250, so it's less than 10% away. As such, the percentage decrease in the volume of the cylinder is greater than 90%.

Re: For a certain cylinder, the diameter equals the height. [#permalink]

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16 Nov 2017, 04:59

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