Acube with a volume of 75cm^3 is dilated by a scale factor of 5. what is the volume of the dilated cube?

To find the volume of the new cube, you will consider that for each dimension you will multiply the dimension by 5 for the scale factor.  In this case there are 3 dimensions that you will apply the scale factor of 5 to.  That means 75 will be multiplied by 5, by 5, and by 5 again.  The new volume will be 9375 cm^3.

We know that
in volume
[the scale factor]=∛{[dilated volume]/[initial volume]}
then
[the scale factor]³=[dilated volume]/[initial volume]
[dilated volume]=[initial volume]*[the scale factor]³
[dilated volume]=[75]*[5]³> 75*125> 9375 cm³

the answer is 9375 cm³