Mathematics: The dimensions of a cube increase by a scale factor of 2. If the resulting cube has a volume of 64 cm3, then what was the length of one edge of the original cube?

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The dimensions of a cube increase by a scale

hailey5129

30.01.2022

The original length of the edges are equal to 2 cm.

Step-by-step explanation:

The volume of a cube is given by the following expression:

V = a^3

Where "a" is the length of each edge of the cube. Assuming that the original cube had a length of "x", then its volume would be:

$V_{original} = x^3$

Since the edges of the cube got scaled by a factor of 2, then the new edges are "2*x" and the volume is:

$V_{new} = (2*x)^3\\V_{new} = 8*x^3\\64 = 8*x^3\\x^3 = \frac{64}{8}\\x^3 = 8\\x = \sqrt[3]{8} = 2$

The original length of the edges are equal to 2 cm.

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