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# A right cylinder and a cube have the same surface area. If the...

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Manager
Joined: 24 May 2016
Posts: 141
A right cylinder and a cube have the same surface area. If the...  [#permalink]

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07 Aug 2016, 02:20
4
00:00

Difficulty:

85% (hard)

Question Stats:

55% (03:25) correct 45% (03:45) wrong based on 70 sessions

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A right cylinder and a cube have the same surface area. If the height of the cylinder is equal to its diameter, then the volume of the cylinder is approximately what percent greater than the volume of the cube?

A) 6%
B) 13%
C) 26%
D) 32%
E) 35%

Manager
Joined: 24 May 2016
Posts: 141
A right cylinder and a cube have the same surface area. If the...  [#permalink]

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Updated on: 07 Aug 2016, 08:11
Here is my go:

Cylinder Surface = 2 π r^2 + 2 π r * 2 r = 2 π r^2 + 4 π r^2 = 6 π r^2
Cube Surface = 6 π r^2

To get one length of the cube:

6 x^2 = 6 π r^2 ; x^2 = π r^2 ; x = r $$\sqrt{π}$$

Cylinder Volume = π r^2 * 2r = 2 π r^3
Cube Volume = x^3 = (r $$\sqrt{π}$$)^3 = r^3 π $$\sqrt{π}$$

Cylinder Volume /Cube Volume = (2 π r^3) / (r^3 π $$\sqrt{π}$$)
= (2 / $$\sqrt{π}$$) * ($$\sqrt{π}$$ / $$\sqrt{π}$$)
= (2 * $$\sqrt{π}$$)) / π

Roughly, this is:

2 * 1.75 / 3.15 = 3.50 / 3.15

Which is between 10% and 15% more.

Please let me know if there is any error in this thought process.

Originally posted by EBITDA on 07 Aug 2016, 08:06.
Last edited by EBITDA on 07 Aug 2016, 08:11, edited 1 time in total.
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Re: A right cylinder and a cube have the same surface area. If the...  [#permalink]

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07 Aug 2016, 08:11
EBITDA wrote:
Here is my go:

Surface Cylinder = 2 π r^2 + 2 π r * 2 r = 2 π r^2 + 4 π r^2 = 6 π r^2
Surface Cube = 6 π r^2

To get one length of the cube:

6 x^2 = 6 π r^2 ; x^2 = π r^2 ; x = r $$\sqrt{π}$$

Volume Cylinder = π r^2 * 2r = 2 π r^3
Volume Cube = x^3 = (r $$\sqrt{π}$$)^3 = r^3 π $$\sqrt{π}$$

Volume Cylinder/Volume Cube = (2 π r^3) / (r^3 π $$\sqrt{π}$$)
= (2/$$\sqrt{π}$$) * ($$\sqrt{π}$$/$$\sqrt{π}$$)
= (2*$$\sqrt{π}$$)) / π

Roughly, this is:

2 * 1.75 / 3.15 = 3.50 / 3.15

Which is between 10% and 15% more.

Please let me know if there is any error in this thought process.

How do you know if it is total surface area or lateral surface area?
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Manager
Joined: 24 May 2016
Posts: 141
A right cylinder and a cube have the same surface area. If the...  [#permalink]

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07 Aug 2016, 08:28
If they meant to refer to the lateral surface, they should have to specify it.
Manager
Joined: 20 Mar 2015
Posts: 59
Location: United States
Concentration: General Management, Strategy
WE: Design (Manufacturing)
A right cylinder and a cube have the same surface area. If the...  [#permalink]

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07 Aug 2016, 13:34
@EBITDA: your approach is correct but it seems you did a calculation mistake. X=pi^1/2 X r= 1.73r (approx)
You have calculated X as r/ (pi^1/2)

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Joined: 12 Dec 2016
Posts: 1546
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
Re: A right cylinder and a cube have the same surface area. If the...  [#permalink]

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20 Dec 2017, 13:12
such math problem really takes time. Particularly, when one make mistakes on calculation, the problem will drive the person into crazy. It happened to me today, and I feel mad because I wasted time on one question.
Re: A right cylinder and a cube have the same surface area. If the...   [#permalink] 20 Dec 2017, 13:12
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