Answer:
The volume of the cube is [tex]\frac{125}{8}[/tex] cubic centimeters ([tex]15.625[/tex] cubic centimeters).
Step-by-step explanation:
First, we must convert the side length into a fraction form:
[tex]s = 2\,\frac{1}{2}\,cm[/tex]
[tex]s = \left(2 +\frac{1}{2}\right)\,cm[/tex]
[tex]s = \left(\frac{4}{2}+\frac{1}{2} \right)\,cm[/tex]
[tex]s = \frac{5}{2}\,cm[/tex]
The decimal form of the side length is:
[tex]s = 2.5\,cm[/tex]
Lastly, we calculate the volume of the cube as a fraction and a decimal:
Fraction
[tex]V = \left(\frac{5}{2}\,cm \right)^{3}[/tex]
[tex]V = \frac{125}{8}\,cm^{3}[/tex]
Decimal
[tex]V = (2.5\,cm)^{3}[/tex]
[tex]V = 15.625\,cm^{3}[/tex]
The volume of the cube is [tex]\frac{125}{8}[/tex] cubic centimeters ([tex]15.625[/tex] cubic centimeters).
