Answer:
The volume of her cube is [tex]15\,\frac{5}{8}[/tex] cubic centimeters.
Step-by-step explanation:
The side length of the cube is [tex]2\,\frac{1}{2}\,cm[/tex], we proceed to convert this value into an entirely rational form:
[tex]s = 2\,\frac{1}{2}\,cm[/tex]
[tex]s = \left(\frac{4}{2}+\frac{1}{2} \right)\,cm[/tex]
[tex]s = \left(\frac{4+1}{2} \right)\,cm[/tex]
[tex]s = \frac{5}{2}\,cm[/tex]
The volume of the cube ([tex]V[/tex]), measured in cubic centimeters, is determined by the following expression:
[tex]V = s^{3}[/tex] (1)
If we know that [tex]s = \frac{5}{2}\,cm[/tex], then the volume of the cube is:
[tex]V = \left(\frac{5}{2}\,cm \right)^{3}[/tex]
[tex]V = \frac{125}{8}\,cm^{3}[/tex]
[tex]V = \left(\frac{120}{8}+\frac{5}{8}\right)\,cm^{3}[/tex]
[tex]V = 15\,\frac{5}{8}\,cm^{3}[/tex]
The volume of her cube is [tex]15\,\frac{5}{8}[/tex] cubic centimeters.
