The volume of a cubical box is 3.375 cubic metres. The length of edge of the box is

Options

A. 75 cm
B. 1.5 m
C. 1.125 m
D. 2.5 m

Answer

To find the length of the edge of a cubical box given its volume, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Volume of a Cube**:
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
where \( a \) is the length of an edge of the cube.

2. **Set Up the Equation**:
Given that the volume of the cube is \( 3.375 \) cubic meters, we can write:
\[ a^3 = 3.375 \]

3. **Calculate the Cube Root**:
To find the length of the edge \( a \), we need to calculate the cube root of \( 3.375 \):
\[ a = \sqrt[3]{3.375} \]

4. **Simplify the Calculation**:
We can express \( 3.375 \) as a fraction to make it easier to calculate:
\[ 3.375 = \frac{3375}{1000} \]
Now, we can find the cube root of both the numerator and the denominator:
\[ a = \frac{\sqrt[3]{3375}}{\sqrt[3]{1000}} \]

5. **Calculate the Cube Roots**:
- The cube root of \( 1000 \) is \( 10 \) because \( 10^3 = 1000 \).
- Now, we need to find the cube root of \( 3375 \). We can factor \( 3375 \):
- \( 3375 = 3^3 \times 5^3 \)
- Therefore, the cube root of \( 3375 \) is:
\[ \sqrt[3]{3375} = 3 \times 5 = 15 \]

6. **Combine the Results**:
Now substituting back, we have:
\[ a = \frac{15}{10} = 1.5 \]

7. **Final Answer**:
Thus, the length of the edge of the cubical box is:
\[ \boxed{1.5 \text{ meters}} \]