Math Problem Statement

Consider a circle whose size can vary. The circumference of the circle is always 2π times as large as its radius. Let r represent the radius of the circle (in feet) and let C represent the circumference of the circle (in feet).

Write a formula that expresses r in terms of C.

Solution

The formula for the circumference CC of a circle in terms of its radius rr is:

C=2πrC = 2\pi r

To express rr in terms of CC, solve for rr:

r=C2πr = \frac{C}{2\pi}

Thus, the formula for the radius rr in terms of the circumference CC is:

r=C2πr = \frac{C}{2\pi}

Would you like a detailed explanation of how this formula was derived?


Here are 5 related questions:

  1. What happens to the radius if the circumference doubles?
  2. How does the area of the circle relate to its circumference?
  3. If the circumference is 31.4 feet, what is the radius?
  4. How can you express the diameter in terms of the circumference?
  5. What is the relationship between radius and area for a circle?

Tip: Remember, the diameter of a circle is always twice the radius!

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Math Problem Analysis

Mathematical Concepts

Geometry
Algebra
Formulas for Circle

Formulas

C = 2πr
r = C / 2π

Theorems

Relationship between Circumference and Radius

Suitable Grade Level

Grades 6-8