A cube with a volume of 75 cm³ is dilated by a factor of 5. What is the volume of the dilated cube? Enter your answer in the box.

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. If the scale factor is greater than 1, the image is an enlargement.  

If a figure is enlarged by a factor of five, the length will be five times greater, the width will be five times greater and the height will be five times greater.The volume will therefore be [tex]5^3[/tex] greater.

Hence
 [tex]V_{dilated}=5^3\cdot V_{initial}, \\ v_{dilated}=5^3\cdot 75=125\cdot 75=9375 cm^3.[/tex]