Question

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

Answer 1

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

Answer 2

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.