The surface area of a cube is 486 sq cm. Find its volume.

Answer

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

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

### Step 2: Set up the equation with the given surface area.
We know the surface area of the cube is 486 sq cm. Therefore, we can set up the equation:
\[ 6s^2 = 486 \]

### Step 3: Solve for \( s^2 \).
To isolate \( s^2 \), divide both sides of the equation by 6:
\[ s^2 = \frac{486}{6} \]
Calculating the right side:
\[ s^2 = 81 \]

### Step 4: Find the value of \( s \).
To find \( s \), we take the square root of both sides:
\[ s = \sqrt{81} \]
Calculating the square root:
\[ s = 9 \, \text{cm} \]

### Step 5: Use the side length to find the volume.
The volume (V) of a cube is given by the formula:
\[ V = s^3 \]
Substituting the value of \( s \):
\[ V = 9^3 \]
Calculating \( 9^3 \):
\[ V = 729 \, \text{cm}^3 \]

### Final Answer:
The volume of the cube is \( 729 \, \text{cm}^3 \).

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