The surface area of a cube is 1350 sq cm. Find the volume of the cube.

Answer

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

### Step-by-Step Solution:

1. **Understand the formula for the surface area of a cube**:
The surface area (SA) of a cube is given by the formula:
\[ SA = 6 \times \text{side}^2 \]

2. **Set up the equation with the given surface area**:
We know the surface area of the cube is 1350 sq cm. Therefore, we can write:
\[ 6 \times \text{side}^2 = 1350 \]

3. **Solve for the side length**:
To find the side length, we first divide both sides of the equation by 6:
\[ \text{side}^2 = \frac{1350}{6} \]
Calculating the right side:
\[ \text{side}^2 = 225 \]

4. **Take the square root to find the side length**:
Now, we take the square root of both sides to find the side length:
\[ \text{side} = \sqrt{225} = 15 \text{ cm} \]

5. **Use the side length to find the volume**:
The volume (V) of a cube is given by the formula:
\[ V = \text{side}^3 \]
Substituting the side length we found:
\[ V = 15^3 \]

6. **Calculate the volume**:
Now we calculate \(15^3\):
\[ V = 15 \times 15 \times 15 = 3375 \text{ cm}^3 \]

### Final Answer:
The volume of the cube is \(3375 \text{ cm}^3\).

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