Answer:
the size of the side of the smaller cube is 15 cm
Step-by-step explanation:
Start by finding what is the side of a cube whose volume is 91125 cm^3.
Since the volume of a cube of side "x" is x^3, then we need to use the cubic root of 91125 cm^3 to find it:
[tex]x = \sqrt[3]{91125\, cm^3} = 45 cm[/tex]
The smaller cube generated by a transformation which involves a scale factor of 1/3 (one third) is going to reduce the side of the cube by a factor of 1/3 , which is the same a dividing the original side measure by 3.
Therefore, the new (smaller) cube is going to have side length of 45 cm divided by 3, which gives:
[tex]\frac{45\,cm}{3} = 15\, cm[/tex]
