Question

D.Question 155 ptsThe lateral area of a cube is 324 square centimeters. Find the volume of the cube.O 972 cm39 cm30 729 cm3O 81 cm3

Answer 1

Step-by-step explanation:

lateral area of cube = 324 square centimeters

Formula for lateral area of cube:

`\text{Lateral area of cube = 4}*\text{ (side)}^2`
`\begin{gathered} 324=4* side^2 \\ \frac{324}{4\text{ }}=\text{ }(4* side^2)/(4) \\ \text{81 = }(4* side^2)/(4) \\ \text{square root both sides:} \\ \sqrt[]{81}\text{ = }\sqrt[]{side^2} \\ \text{side = 9 cm} \end{gathered}`

We apply volume of a cube:

`\text{Volume of cube = (side)}^3`
`\begin{gathered} \text{Volume of a cube = (9)}^3 \\ \text{Volume of a cube = }729cm^3\text{ (option C)} \end{gathered}`