If the volume of two cubes are in the ratio 27 :1, the ratio of their edge is :

Options

A. `3:1`
B. `27:1`
C. `1:3`
D. `1:27`

Answer

To solve the problem, we need to find the ratio of the edges of two cubes given that their volumes are in the ratio of 27:1.

### Step-by-Step Solution:

1. **Understanding the Volume of a Cube**:
The volume \( V \) of a cube with edge length \( a \) is given by the formula:
\[ V = a^3 \]

2. **Setting Up the Volume Ratio**:
Let the edge lengths of the two cubes be \( a_1 \) and \( a_2 \). According to the problem, the volumes of the cubes are in the ratio:
\[ \frac{V_1}{V_2} = \frac{27}{1} \]
This can be expressed in terms of the edge lengths:
\[ \frac{a_1^3}{a_2^3} = \frac{27}{1} \]

3. **Taking the Cube Root**:
To find the ratio of the edge lengths, we take the cube root of both sides:
\[ \frac{a_1}{a_2} = \sqrt[3]{\frac{27}{1}} = \sqrt[3]{27} = 3 \]

4. **Final Ratio of Edge Lengths**:
Therefore, the ratio of the edges \( a_1 \) to \( a_2 \) is:
\[ \frac{a_1}{a_2} = 3:1 \]

### Conclusion:
The ratio of the edges of the two cubes is \( 3:1 \).