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A cube and a rectangular solid are equal in volume. If the lengths of

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A cube and a rectangular solid are equal in volume. If the lengths of  [#permalink]

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New post 08 Jan 2019, 04:14
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A cube and a rectangular solid are equal in volume. If the lengths of the edges of the rectangular solid are 4, 8, and 16, what is the length of an edge of the cube?

A. 4
B. 8
C. 12
D. 16
E. 64

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Re: A cube and a rectangular solid are equal in volume. If the lengths of  [#permalink]

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New post 08 Jan 2019, 04:25
Bunuel wrote:
A cube and a rectangular solid are equal in volume. If the lengths of the edges of the rectangular solid are 4, 8, and 16, what is the length of an edge of the cube?

A. 4
B. 8
C. 12
D. 16
E. 64


vol= 4*8*16 = 512
side of cube = (512)^1/3
= 8 IMO B
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Re: A cube and a rectangular solid are equal in volume. If the lengths of  [#permalink]

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New post 08 Jan 2019, 05:00
1
Bunuel wrote:
A cube and a rectangular solid are equal in volume. If the lengths of the edges of the rectangular solid are 4, 8, and 16, what is the length of an edge of the cube?

A. 4
B. 8
C. 12
D. 16
E. 64


Volume of a cube = Side^3
Volume of a rectangular solid = Length*Breadth*Height = 4*8*16 = 2^9

Given \(Side^3 = 2^9 = (2^3)^3 = 8^3\)

\(Side = 8\)
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Re: A cube and a rectangular solid are equal in volume. If the lengths of  [#permalink]

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New post 17 Jan 2019, 23:25
Geometric mean.
3√(\(2^2·2^3·2^4\))=\(2^{9/3}\)=\(2^3\)=8
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Re: A cube and a rectangular solid are equal in volume. If the lengths of &nbs [#permalink] 17 Jan 2019, 23:25
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A cube and a rectangular solid are equal in volume. If the lengths of

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