The surface area of a cube is `864 cm^(2)`. Find its volume

Answer

To find the volume of a cube when given its surface area, we can follow these steps:

### Step 1: Understand the formula for the surface area of a cube.
The surface area \( A \) of a cube is given by the formula:
\[ A = 6s^2 \]
where \( s \) is the length of one side of the cube.

### Step 2: Set up the equation using the given surface area.
We know from the problem that the surface area is \( 864 \, \text{cm}^2 \). Therefore, we can set up the equation:
\[ 6s^2 = 864 \]

### Step 3: Solve for \( s^2 \).
To isolate \( s^2 \), divide both sides of the equation by 6:
\[ s^2 = \frac{864}{6} \]
Calculating the right side:
\[ s^2 = 144 \]

### Step 4: Find the length of one side \( s \).
Now, take the square root of both sides to find \( s \):
\[ s = \sqrt{144} \]
Calculating the square root:
\[ s = 12 \, \text{cm} \]

### Step 5: Use the side length to find the volume of the cube.
The volume \( V \) of a cube is given by the formula:
\[ V = s^3 \]
Substituting the value of \( s \):
\[ V = 12^3 \]
Calculating \( 12^3 \):
\[ V = 1728 \, \text{cm}^3 \]

### Final Answer:
The volume of the cube is \( 1728 \, \text{cm}^3 \).

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