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Can you explain step by step how "a cube has a side length of 10 cm. The cube is dilated by a scale factor of 5. How does the volume of the new cube compare to the volume of the original cube?" The answer is the volume is 125 times the volume of the original cube but how is this the answer.



Answer :

facundo3141592

After the dilation, the new volume of the cube is 125 times the original volume of the cube.

How does the new volume compare to the original volume?

Remember that for a cube of sidelength S, the volume is written as:

V = S^3

If we apply a dilation of scale factor 5 to the cube, then the new sidelength of the cube is 5*S

Replacing that in the volume formula we will get the volume of the dilated cube, it is:

V' = (5*S)^3

V' = 5^3*S^3

V' = 125*S^3

Where S^3 is the original volume, so we can write:

V' = 125*V

So the new volume is 125 times the original volume.

Learn more about dilations:

https://brainly.com/question/3457976

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