The ratio of circumference and diameter of a circle is $3 : 5$. If the circumference is $6 ext{ cm}$, then the radius of the circle is:

Question

The ratio of circumference and diameter of a circle is $3 : 5$. If the circumference is $6 	ext{ cm}$, then the radius of the circle is:

Accepted Answer

**Solution:**

1. Given the ratio of circumference to diameter is $3 : 5$.

2. Let the circumference be $3x$ and diameter be $5x$.

3. Given circumference = $6 	ext{ cm}$, so:
   $$3x = 6 \implies x = 2$$

4. Diameter = $5x = 5 	imes 2 = 10 	ext{ cm}$

5. Radius $r = \frac{	ext{diameter}}{2} = \frac{10}{2} = 5 	ext{ cm}$

6. However, the ratio $\frac{	ext{circumference}}{	ext{diameter}} = \frac{3}{5} = 0.6$ which contradicts the known ratio $\pi \approx 3.1416$.

7. Since the ratio given is $3:5$, the circumference is less than the diameter, which is not possible for a circle.

8. But since the question asks for radius based on the given ratio and circumference, we proceed with the calculation:

- Using the formula for circumference: $$C = 2\pi r$$
   - Given $C = 6$, so:
     $$6 = 2\pi r \implies r = \frac{6}{2\pi} = \frac{3}{\pi} \approx \frac{3}{3.1416} \approx 0.955 	ext{ cm}$$

9. This radius does not match any option exactly.

10. Alternatively, if we interpret the ratio as circumference : diameter = 3 : 5, then circumference = 6 cm corresponds to diameter = 10 cm, so radius = 5 cm.

**Answer:** $5 	ext{ cm}$

**Note:** The ratio given contradicts the actual ratio $\pi$, but based on the question's data, the radius is $5 	ext{ cm}$.

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