**10 POINTS PLEASE HELP!!**
A cube is dilated by a factor of 4. By what factor does its volume increase? Complete the explanation of your reasoning.

The volume increases by a factor of . When the cube is dilated, each side length is increased by (select), so the volume is increased by (select) the dilation factor.

The volume increases by a factor or 64. When the cube is dilated, each side length is increased by 4, so the volume is increased by 64.

Step-by-step explanation:

Let L represents the Length of the cube before it's dilated.

Volume, V1 = Length * Length * Length

Volume, V1 = L * L * L

Volume, V1 = L³

When the cube is dilated by a factor of 4.

The new Length becomes 4L.

The new volume is calculated as thus.

New Volume, V2 = 4L * 4L * 4L

New Volume, V2 = 64L³

Dividing the new volume by the old volume gives the increment factor.

Factor = New Volume ÷ Old Volume

Factor = V2/V1

Factor = 64L³/L³

Factor = 64.

Hence, when the sides of the cube is dilated by 4, the volume increases by a factor of 64.

Filling the gap of the given sentence;

"The volume increases by a factor or 64. When the cube is dilated, each side length is increased by 4, so the volume is increased by 64"

step-by-step explanation:

the options are kind of confusing. i can tell you what i see going on here when i look at the graph.

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