The volume of a cube is 274.625 `cm^(3)`. Find its side (in cm).

Options

A. 7.5
B. 6.5
C. 5.5
D. 3.5

Answer

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

### Step-by-Step Solution:

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.

2. **Set up the equation**:
Given that the volume of the cube is \( 274.625 \, \text{cm}^3 \), we can set up the equation:
\[ \text{side}^3 = 274.625 \]

3. **Solve for the side**:
To find the side, we need to take the cube root of both sides:
\[ \text{side} = \sqrt[3]{274.625} \]

4. **Calculate the cube root**:
We can calculate \( \sqrt[3]{274.625} \). This can be done using a calculator or by estimating.

- First, we can estimate the cube root by finding nearby perfect cubes:
- \( 6^3 = 216 \)
- \( 7^3 = 343 \)

Since \( 274.625 \) is between \( 216 \) and \( 343 \), we know the side length is between \( 6 \) and \( 7 \).

5. **Refine the estimate**:
To get a more precise value, we can try \( 6.5 \):
\[ 6.5^3 = 6.5 \times 6.5 \times 6.5 = 274.625 \]

Therefore, we find that:
\[ \text{side} = 6.5 \, \text{cm} \]

### Final Answer:
The side of the cube is \( 6.5 \, \text{cm} \).

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