Explanation:
lateral area of cube = 324 square centimeters
Formula for lateral area of cube:
[tex]\text{Lateral area of cube = 4}\times\text{ (side)}^2[/tex][tex]\begin{gathered} 324=4\times side^2 \\ \frac{324}{4\text{ }}=\text{ }\frac{4\times side^2}{4} \\ \text{81 = }\frac{4\times side^2}{4} \\ \text{square root both sides:} \\ \sqrt[]{81}\text{ = }\sqrt[]{side^2} \\ \text{side = 9 cm} \end{gathered}[/tex]
We apply volume of a cube:
[tex]\text{Volume of cube = (side)}^3[/tex][tex]\begin{gathered} \text{Volume of a cube = (9)}^3 \\ \text{Volume of a cube = }729cm^3\text{ (option C)} \end{gathered}[/tex]
