Question

A cube has a volume of 91125 cm cubed. A smaller cube is generated under a transformation of scale factor 1/3. What is the length of the side of the smaller cube?

Answer 1

the size of the side of the smaller cube is 15 cm

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:

`x = \sqrt[3]{91125\, cm^3} = 45 cm`

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:

`(45\,cm)/(3) = 15\, cm`