Question

Marie can find the volume of a cube by using the formula V = s³, where s represents the side length of the cube. If Marie’s cube has a side length of 2 1\2

centimeters, what is the volume of her cube? Show your work. Make sure that you include the correct unit of measure in your answer.

Answer 1

The volume of her cube is
`15\,(5)/(8)` cubic centimeters.

Explanation:

The side length of the cube is
`2\,(1)/(2)\,cm`, we proceed to convert this value into an entirely rational form:

`s = 2\,(1)/(2)\,cm`

`s = \left((4)/(2)+(1)/(2) \right)\,cm`

`s = \left((4+1)/(2) \right)\,cm`

`s = (5)/(2)\,cm`

The volume of the cube (
`V`), measured in cubic centimeters, is determined by the following expression:

`V = s^(3)` (1)

If we know that
`s = (5)/(2)\,cm`, then the volume of the cube is:

`V = \left((5)/(2)\,cm \right)^(3)`

`V = (125)/(8)\,cm^(3)`

`V = \left((120)/(8)+(5)/(8)\right)\,cm^(3)`

`V = 15\,(5)/(8)\,cm^(3)`

The volume of her cube is
`15\,(5)/(8)` cubic centimeters.