The ratio of the radii of two wheels is 3:4. The ratio of their circumference is

Options

A. `4:3`
B. `3:4`
C. `2:3`
D. `3:2`

Answer

To solve the problem, we need to find the ratio of the circumferences of two wheels given the ratio of their radii.

### Step-by-Step Solution:

1. **Identify the given ratio of the radii**:
The ratio of the radii of the two wheels is given as 3:4.
Let's denote the radius of the first wheel as \( r_1 = 3x \) and the radius of the second wheel as \( r_2 = 4x \), where \( x \) is a common multiplier.

2. **Use the formula for circumference**:
The circumference \( C \) of a circle (or wheel) is given by the formula:
\[ C = 2\pi r \]
Therefore, the circumference of the first wheel \( C_1 \) is:
\[ C_1 = 2\pi r_1 = 2\pi (3x) = 6\pi x \]
And the circumference of the second wheel \( C_2 \) is:
\[ C_2 = 2\pi r_2 = 2\pi (4x) = 8\pi x \]

3. **Find the ratio of the circumferences**:
Now we can find the ratio of the circumferences \( C_1 \) and \( C_2 \):
\[ \text{Ratio of circumferences} = \frac{C_1}{C_2} = \frac{6\pi x}{8\pi x} \]
The \( \pi x \) terms cancel out:
\[ \frac{C_1}{C_2} = \frac{6}{8} = \frac{3}{4} \]

4. **Conclusion**:
Therefore, the ratio of the circumferences of the two wheels is 3:4.

### Final Answer:
The ratio of their circumferences is **3:4**.