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 of a circle in terms of its radius is:
To express in terms of , solve for :
Thus, the formula for the radius in terms of the circumference is:
Would you like a detailed explanation of how this formula was derived?
Here are 5 related questions:
- What happens to the radius if the circumference doubles?
- How does the area of the circle relate to its circumference?
- If the circumference is 31.4 feet, what is the radius?
- How can you express the diameter in terms of the circumference?
- 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