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

A cube has a base area of 9 cm².

Is it possible to calculate the volume of the cube? If so, what is it?

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: $27$