Bunuel wrote:
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
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
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