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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

Question

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

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Solution

1. Break Down the Problem

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

2. Relevant Concepts

We need to isolate r r in the equation: r=C2π r = \frac{C}{2\pi}

3. Analysis and Detail

Substituting the given circumference (40.8 mm) into the formula, we get: r=40.82π r = \frac{40.8}{2\pi}

Calculating the value:

  1. Calculate 2π 2\pi :

    • 2π6.2832 2\pi \approx 6.2832
  2. Substitute and calculate r r : r40.86.28326.5 mm r \approx \frac{40.8}{6.2832} \approx 6.5 \text{ mm}

4. Verify and Summarize

To verify, we calculate the circumference using r6.5 mm r \approx 6.5 \text{ mm} : C=2π(6.5)40.8 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 6.5 mm.

This problem has been solved

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