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Director  Joined: 01 May 2007
Posts: 639
If the volume of cube A is twice that of cube B, the side of  [#permalink]

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3
2 00:00

Difficulty:   15% (low)

Question Stats: 76% (01:20) correct 24% (01:49) wrong based on 254 sessions

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If the volume of cube A is twice that of cube B, the side of cube A is how many time that of cube B?

A. 1/2
B. $$\sqrt{2}$$
C. $$3\sqrt{2}$$
D. 2
E. 8

Originally posted by jimmyjamesdonkey on 22 Jul 2007, 08:51.
Last edited by Bunuel on 22 May 2014, 02:42, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Senior Manager  Joined: 04 Jun 2007
Posts: 259
Re: PS: Volume of a cube  [#permalink]

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jimmyjamesdonkey wrote:
If the volume of cube A is twice that of cube B, the side of cube A is how many time that of cube B?

1) 1/2
2) cubed rt(2)
3) 3*cubed rt(2)
4) 2
5) 8

OA to follow. side of cube A = a
side of cube B = b

a^3 = 2 * b^3
a = cubed rt(2) * b

Hence, B.
Director  Joined: 01 May 2007
Posts: 639

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B is correct, incorrect approach to solve.
Director  Joined: 01 May 2007
Posts: 639

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Senior Manager  Joined: 08 Jun 2007
Posts: 422
Re: PS: Volume of a cube  [#permalink]

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jimmyjamesdonkey wrote:
If the volume of cube A is twice that of cube B, the side of cube A is how many time that of cube B?

1) 1/2
2) cubed rt(2)
3) 3*cubed rt(2)
4) 2
5) 8

OA to follow. B : This looked like a plain vanilla. Was there any trick involved??
CEO  Joined: 07 Jul 2004
Posts: 3004
Location: Singapore

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Let side of cube A be x, side of cube B be y

Volume of A = x^3
Volue of B = y^3

x^3 = 2y^3
x = 2^1/3(y)

So the side of A is cube root (2) of B
Director  Joined: 08 Jun 2005
Posts: 887

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ywilfred is correct:

X = one cube
Y = second cube

x^3 = y^3*2 ---> (one volume is twice the other volume)

3sqrt(2)^3 = 2

x^3 = y^3*3sqrt(2)^3

x^3 = (y*3sqrt(2))^3 ---> the same way that 2^2*3^2 = 6^2

x = y*3sqrt(2)

the answer is (B) = cubed rt(2) = 3sqrt(2) Intern  Joined: 14 May 2014
Posts: 39
Re: If the volume of cube A is twice that of cube B, the side of  [#permalink]

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Volume of cube is directly proportional to the cube of side
Volume of CubeA/Volume of Cube B = [Side of cube A/side of cube B]^3

in this question
Volume of A/Volume of B = 2

[Side of cube A/side of cube B]^3 = 2

Side of cube A/side of cube B = cubic root (2)

Side of cube A = cubic root (2) * Side of B

Math Expert V
Joined: 02 Sep 2009
Posts: 62619
Re: If the volume of cube A is twice that of cube B, the side of  [#permalink]

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jimmyjamesdonkey wrote:
If the volume of cube A is twice that of cube B, the side of cube A is how many time that of cube B?

A. 1/2
B. $$\sqrt{2}$$
C. $$3\sqrt{2}$$
D. 2
E. 8

3-D Geometry Questions Directory: 3-d-geometry-questions-171024.html
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Director  G
Joined: 23 Jan 2013
Posts: 511
Schools: Cambridge'16
If the volume of cube A is twice that of cube B, the side of  [#permalink]

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any cubes are similar each other meaning that the ratio of theirs volumes is third degree of their side's ratio, so

a^3/2b^3=sqrt^3 of a^3/sqrt^3 of (2b)^3=a/sqrt^3 of 2*b

B
SVP  Status: The Best Or Nothing
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Posts: 1713
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If the volume of cube A is twice that of cube B, the side of  [#permalink]

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Let volume of cube B = 1 = 1 * 1 *1

Then volume of cube A = 2 $$= 2^{\frac{1}{3}} * 2^{\frac{1}{3}} * 2^{\frac{1}{3}}$$

Dimension of Cube A is $$2^{\frac{1}{3}}$$ times that of dimension of cube B

Manager  S
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Concentration: Entrepreneurship, Marketing
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Re: If the volume of cube A is twice that of cube B, the side of  [#permalink]

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Concept is Cube
Cube _ 6 Sides , Volume is S^3 , Given 2 Cubes
S^3 = 2 x S^3
???Confused
Changing the variables as two Different Cubes
a^3 = 2 b^3 ( A is twice that of B)
a = ? ??
a x a^2 = 2 x b^3
a = 2 x b^3 /a^2 ?????
Next? ?

Is my thought process is right??
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1713
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If the volume of cube A is twice that of cube B, the side of  [#permalink]

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kanusha wrote:
Concept is Cube
Cube _ 6 Sides , Volume is S^3 , Given 2 Cubes
S^3 = 2 x S^3
???Confused
Changing the variables as two Different Cubes
a^3 = 2 b^3 ( A is twice that of B)
a = ? ??
a x a^2 = 2 x b^3
a = 2 x b^3 /a^2 ?????
Next? ?

Is my thought process is right??

Instead of taking 2 variables, just try plugins... Please look at posts above
Manager  B
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 105
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
Re: If the volume of cube A is twice that of cube B, the side of  [#permalink]

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1
kanusha wrote:
Concept is Cube
Cube _ 6 Sides , Volume is S^3 , Given 2 Cubes
S^3 = 2 x S^3
???Confused
Changing the variables as two Different Cubes
a^3 = 2 b^3 ( A is twice that of B)
a = ? ??
a x a^2 = 2 x b^3
a = 2 x b^3 /a^2 ?????
Next? ?

Is my thought process is right??

Here you have to find the relation between Side od Cube A and Side of Cube B

Let Sa = side of cube A
And Sb = Side of cube B

given, Va = 2* Vb

(Sa^3) = 2* (Sb^3)--------------- Till this step you are correct. See the below explanation to clear the doubt.

Taking Cube root on both sides

Sa = 2^(1/3) * Sb

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Posts: 778
Location: United States
GMAT 1: 660 Q49 V31
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Re: If the volume of cube A is twice that of cube B, the side of  [#permalink]

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jimmyjamesdonkey wrote:
If the volume of cube A is twice that of cube B, the side of cube A is how many time that of cube B?

A. 1/2
B. $$\sqrt{2}$$
C. $$3\sqrt{2}$$
D. 2
E. 8

Volume A= 2 Volume B

Side^3 (A) = 2 Side ^3 (B)
Side (A) = 2 ^1/3X Side (B)

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I welcome critical analysis of my post!! That will help me reach 700+ Re: If the volume of cube A is twice that of cube B, the side of   [#permalink] 25 May 2016, 07:51
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