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13 Sep 2017, 21:49
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D
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Difficulty:
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94% (00:46) correct
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Cube A has a volume of a cubic inches. If each side of Cube B is twice as long as each side of Cube A, then what is the volume of Cube B?
A. 2a
B. 4a
C. 6a
D. 8a
E. 16a
A. 2a
B. 4a
C. 6a
D. 8a
E. 16a
13 Sep 2017, 22:35
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Volume of cube= L^3
Volume of cube A= a cubic inches
a= L^3
L= a^1/3
Side of cube B is twice as long as side of A.
Side of Cube B= l= 2*(a^1/3)
Volume of Cube B= l^3
= 2^3 * (a^1/3)^3
=8*a
Hence Answer is option D.
Kudos if it helps.
Volume of cube A= a cubic inches
a= L^3
L= a^1/3
Side of cube B is twice as long as side of A.
Side of Cube B= l= 2*(a^1/3)
Volume of Cube B= l^3
= 2^3 * (a^1/3)^3
=8*a
Hence Answer is option D.
Kudos if it helps.
Bunuel
Volume of Cube A = a = \(s * s* s\).
Cube B = (2s * 2s * 2s), or 8(s * s * s)
Substitute a for (s * s * s): volume of Cube B = 8a
OR
Let Cube A have sides = 1.
Volume is (1*1*1) = a
Each of Cube B's sides is twice as long as Cube A's sides.
Cube B has sides = 2.
Volume of B is
(2*1) * (2*1) * (2*1), or
(2*2*2)(1*1*1).
Substitute a for (1*1*1):
(2*2*2)(a) = 8a, is volume of Cube B
Basically: For dilation, to get resultant volume, multiply the volume of the original by the multiplier cubed -- because each length is scaled up by the multiplier, and volume = (length * length * length).
Multiplier is 2
2\(^3\) = 8
Volume of Cube A = a, so
volume of Cube B = 8a
ANSWER D
