Calculate Cube Volume from 9 cm² Base Area: Step-by-Step Solution

To determine if we can calculate the volume of the cube, let's start by analyzing the given information:

1. The base area of the cube is given as $9 \, \text{cm}^2$. In a cube, each face is a square, so this area corresponds to the area of one face.
2. To find the side length $s$ of the square face, use the formula for the area of a square: $A = s^2$.
3. Set up the equation based on the given area: $s^2 = 9$.
4. Solve for $s$ by taking the square root of both sides: $s = \sqrt{9} = 3 \, \text{cm}$.
5. Now that we have the side length $s$, calculate the volume $V$ of the cube using the formula for the volume of a cube: $V = s^3$.
6. Substitute $s = 3 \, \text{cm}$ into the volume formula: $V = 3^3 = 27 \, \text{cm}^3$.

Therefore, the volume of the cube is $27 \, \text{cm}^3$.

Among the given choices, the correct answer is:

• Choice 3: $27$