To find the radius and diameter of Circle E given its circumference, we can use the formulas for circumference and relationships between the radius, diameter, and circumference of a circle.

Formulas:

1. Circumference (C) = 2 * π * r (where r is the radius)
2. Diameter (d) = 2 * r

Given that the circumference (C) is 52 cm and using π ≈ 3.14, we can solve for the radius (r) first.

Step 1: Find the radius

We know that: $C = 2 \cdot \pi \cdot r$ Substitute the given values: $52 = 2 \cdot 3.14 \cdot r$ $52 = 6.28 \cdot r$ Now solve for $r$: $r = \frac{52}{6.28} \approx 8.28 \text{ cm}$

Step 2: Find the diameter

Now that we have the radius, we can find the diameter using the formula $d = 2 \cdot r$: $d = 2 \cdot 8.28 \approx 16.56 \text{ cm}$

Summary:

• Radius ≈ 8.28 cm
• Diameter ≈ 16.56 cm
• Circumference = 52 cm (as given)

Would you like more details or clarification on any step?

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Related Questions:

1. How does the value of pi affect the measurements of a circle?
2. If the radius of a circle was doubled, how would that affect the circumference and diameter?
3. What would happen if the circumference was 100 cm? How would the radius and diameter change?
4. How is the relationship between the radius and diameter important in solving problems related to circles?
5. Can the formula for circumference be rearranged to solve for the diameter instead of the radius?

Tip:

When calculating with π, using a more precise value (e.g., 3.14159) will give slightly more accurate results.