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If the volume of cube A is twice that of cube B, the side of

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Director
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If the volume of cube A is twice that of cube B, the side of [#permalink] New post 22 Jul 2007, 08:51
00:00
A
B
C
D
E

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  5% (low)

Question Stats:

77% (01:53) correct 23% (00:53) wrong based on 73 sessions
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[3]{2}
C. 3\sqrt[3]{2}
D. 2
E. 8
[Reveal] Spoiler: OA

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.
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Re: PS: Volume of a cube [#permalink] New post 22 Jul 2007, 09:45
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.
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 [#permalink] New post 22 Jul 2007, 09:54
B is correct, incorrect approach to solve.
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 [#permalink] New post 22 Jul 2007, 10:01
Nevermind - misread your answer. You got it.
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Re: PS: Volume of a cube [#permalink] New post 23 Jul 2007, 18:13
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??
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 [#permalink] New post 23 Jul 2007, 18:17
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
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 [#permalink] New post 23 Jul 2007, 20:02
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)

:-D
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Re: If the volume of cube A is twice that of cube B, the side of [#permalink] New post 21 May 2014, 09:02
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

Hence Answer is B
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Re: If the volume of cube A is twice that of cube B, the side of [#permalink] New post 22 May 2014, 02:43
Expert's post
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[3]{2}
C. 3\sqrt[3]{2}
D. 2
E. 8


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If the volume of cube A is twice that of cube B, the side of [#permalink] New post 10 Oct 2014, 21:36
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
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Re: If the volume of cube A is twice that of cube B, the side of [#permalink] New post 15 Oct 2014, 19:05
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

Answer = B
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Re: If the volume of cube A is twice that of cube B, the side of [#permalink] New post 23 Oct 2014, 07:39
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? :idea: ?

Is my thought process is right??
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Re: If the volume of cube A is twice that of cube B, the side of [#permalink] New post 23 Oct 2014, 21:28
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? :idea: ?

Is my thought process is right??



Instead of taking 2 variables, just try plugins... Please look at posts above
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Re: If the volume of cube A is twice that of cube B, the side of [#permalink] New post 23 Oct 2014, 21:39
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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? :idea: ?

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


Therefore answer is B
Re: If the volume of cube A is twice that of cube B, the side of   [#permalink] 23 Oct 2014, 21:39
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