Dino wants to find the length of the radius of a circle with circumference 40.8 mm long.The length of the radius is closest to

1. Break Down the Problem

To find the radius of a circle given its circumference, we can use the formula: $C = 2\pi r$ where $C$ is the circumference and $r$ is the radius.

2. Relevant Concepts

We need to isolate $r$ in the equation: $r = \frac{C}{2\pi}$

3. Analysis and Detail

Substituting the given circumference (40.8 mm) into the formula, we get: $r = \frac{40.8}{2\pi}$

Calculating the value:

1. Calculate $2\pi$:

   • $2\pi \approx 6.2832$

2. Substitute and calculate $r$: $r \approx \frac{40.8}{6.2832} \approx 6.5 \text{ mm}$

4. Verify and Summarize

To verify, we calculate the circumference using $r \approx 6.5 \text{ mm}$: $C = 2\pi(6.5) \approx 40.8 \text{ mm}$ The calculations confirm that our radius estimation is accurate.

Final Answer

The length of the radius is closest to $6.5$ mm.