Find the side of a cube whose volume is `1331/216 m^(3)`

Options

A. `11/6m`
B. `11/4m`
C. `9/7m`
D. `9/4m`

Answer

To find the side of a cube whose volume is \( \frac{1331}{216} \, m^3 \), we can follow these steps:

### Step 1: Understand the formula for the volume of a cube
The volume \( V \) of a cube is given by the formula:
\[ V = \text{side}^3 \]
where "side" is the length of one edge of the cube.

### Step 2: Set up the equation
Given that the volume of the cube is \( \frac{1331}{216} \, m^3 \), we can set up the equation:
\[ \text{side}^3 = \frac{1331}{216} \]

### Step 3: Take the cube root of both sides
To find the side length, we take the cube root of both sides:
\[ \text{side} = \sqrt[3]{\frac{1331}{216}} \]

### Step 4: Simplify the cube root
We can simplify \( \frac{1331}{216} \) by finding the cube roots of the numerator and denominator separately:
- The cube root of \( 1331 \) is \( 11 \) because \( 11 \times 11 \times 11 = 1331 \).
- The cube root of \( 216 \) is \( 6 \) because \( 6 \times 6 \times 6 = 216 \).

Thus, we can rewrite the expression:
\[ \text{side} = \frac{\sqrt[3]{1331}}{\sqrt[3]{216}} = \frac{11}{6} \]

### Step 5: Final answer
Therefore, the side of the cube is:
\[ \text{side} = \frac{11}{6} \, m \]