The surface area of a cube is 726 sq cm. Find the volume of the cube.

Options

A. `1331 cm^(3) `
B. `1232 cm^(3) `
C. `1626 cm^(3) `
D. `1836 cm^(3) `

Answer

To solve the problem of finding the volume of a cube given its surface area, 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:
\[ SA = 6a^2 \]
where \( a \) is the length of one side of the cube.

2. **Set up the equation using the given surface area**:
We know from the problem that the surface area of the cube is 726 sq cm. Therefore, we can set up the equation:
\[ 6a^2 = 726 \]

3. **Solve for \( a^2 \)**:
To isolate \( a^2 \), divide both sides of the equation by 6:
\[ a^2 = \frac{726}{6} \]
Simplifying this gives:
\[ a^2 = 121 \]

4. **Find \( a \)**:
To find the length of one side of the cube, take the square root of both sides:
\[ a = \sqrt{121} = 11 \text{ cm} \]

5. **Calculate the volume of the cube**:
The volume (V) of a cube is given by the formula:
\[ V = a^3 \]
Substituting the value of \( a \):
\[ V = 11^3 = 11 \times 11 \times 11 \]
Calculating this gives:
\[ V = 1331 \text{ cm}^3 \]

### Final Answer:
The volume of the cube is \( 1331 \text{ cm}^3 \).

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