Cubes: Express using

In this problem, we are tasked with expressing the volume of a cube given its side length $a$.

To find the volume of the cube, we use the standard volume formula for a cube, which is given by:

$V = \text{side length}^3$

Since the side length of this cube is $a$, we substitute $a$ into the formula:

$V = a^3$

Thus, the volume of the cube in terms of $a$ is $a^3$.

We compare this with the provided answer choices:

• Choice 1: $a^3$
• Choice 2: $6a^3$
• Choice 3: $6a^2$
• Choice 4: $a^2$

Our computed volume $a^3$ matches Choice 1.

Therefore, the correct choice is: $a^3$.

To solve this problem, we'll determine the surface area using the formula for a cube:

• Step 1: Identify the given information — Each side of the cube is $X$.
• Step 2: Recall the surface area formula — For a cube, it is $6 \times (\text{side length})^2$.
• Step 3: Substitute the side length $X$ into the formula.

Now, let's proceed with the solution:
Step 1: The cube has each side $= X$.
Step 2: The surface area formula for a cube is given by $6 \times (\text{side length})^2$.
Step 3: Substituting $X$ for the side length, we find the surface area is $6 \times X^2$.

Therefore, the surface area of the cube in terms of $X$ is $\mathbf{6X^2}$.

To solve this problem, we'll recall the following relevant formula:

• The surface area of a cube is given by the formula: $\text{Surface Area} = 6a^2$.

Let's break down the solution in steps:

Step 1: Identify the characteristic of the cube.
A cube is a three-dimensional shape with six identical square faces.

Step 2: Determine the area of one face.
Each face of the cube is a square with side length $a$, so the area of one face is $a^2$.

Step 3: Calculate the total surface area.
Since a cube has six identical faces, the total surface area is six times the area of one face:

$\text{Surface Area} = 6 \times a^2 = 6a^2$

Therefore, the surface area of the cube in terms of $a$ is $6a^2$.