Solving for the volume of the cube.
Recall the formula for solving the volume of the cube.
[tex]\begin{gathered} V_{\text{cube}}=s^3 \\ \text{where} \\ s\text{ is the side length of the cube} \end{gathered}[/tex]
Given a side length of 7 units, substitute s = 7, and we have
[tex]\begin{gathered} V_{\text{cube}}=s^3 \\ V_{\text{cube}}=(7)^3 \\ V_{\text{cube}}=343 \end{gathered}[/tex]
Therefore, the volume of the cube is equal to 343 cubic units.
Solving for the side length of the square.
Recall the area of the square
[tex]\begin{gathered} A_{\text{square}}=s^2 \\ \text{where} \\ s\text{ is the side length of the given square} \end{gathered}[/tex]
Given that the area of the square is equal to 13 square inches, substitute A = 13 and we get
[tex]\begin{gathered} A_{\text{square}}=s^2 \\ 13=s^2 \\ \\ \text{Take the square root of both sides} \\ \sqrt[]{13}=\sqrt[]{s^2}^{} \\ s=\sqrt[]{13} \\ s\approx3.6 \end{gathered}[/tex]
Therefore, the side length of the square is the square root of 13 units or approximately 3.6 units
