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

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"