Math Problem Statement

The circumference of a circle is approximately 56.5 inches. What is the radius of the circle? Use 3.14 for pi. Round to the nearest whole number.

Solution

The formula for the circumference of a circle is:

C=2πrC = 2\pi r

Where:

  • CC is the circumference,
  • π\pi is approximately 3.14,
  • rr is the radius.

Given that the circumference C=56.5C = 56.5 inches and π=3.14\pi = 3.14, we can solve for the radius rr as follows:

r=C2πr = \frac{C}{2\pi}

Substitute the given values:

r=56.52×3.14r = \frac{56.5}{2 \times 3.14}

Now calculate:

r=56.56.289.0r = \frac{56.5}{6.28} \approx 9.0

Therefore, the radius of the circle is approximately 9 inches.

Would you like more details or further clarifications?

Here are 5 related questions you might find interesting:

  1. What would be the area of the circle with this radius?
  2. How would the radius change if the circumference were doubled?
  3. What is the diameter of the circle based on the calculated radius?
  4. How would you calculate the circumference if you were given the radius directly?
  5. How does the value of π\pi affect the accuracy of the result?

Tip: Always ensure you use consistent units when solving geometric problems involving circles.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circles
Circumference
Radius

Formulas

C = 2πr (Circumference formula)

Theorems

Properties of Circles

Suitable Grade Level

Grades 6-8