The circumference *C* of a circle is a function of its radius given by *C*(*r*)=2*πr*

**a.** Express the radius of a circle as a function of its circumference. Call this function *r*(*C*)

Enter the exact answer. Enclose numerators and denominators in parentheses. For example, (*a*−*b*)/(1+*n*). r(C)=? 

We are given the equation for the circumference of a circle as a function of its radius:

\[
C(r) = 2\pi r
\]

We are tasked with finding the radius \( r \) as a function of the circumference \( C \). To do this, we need to solve for \( r \) in terms of \( C \).

Starting with the equation for circumference:
\[
C = 2\pi r
\]

Solve for \( r \) by dividing both sides of the equation by \( 2\pi \):

\[
r = \frac{C}{2\pi}
\]

Thus, the radius as a function of the circumference is:

\[
r(C) = \frac{C}{2\pi}
\]

### Final Answer:

\[
r(C) = \frac{C}{(2\pi)}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the radius if the circumference is 10 units?
2. How would the formula change if the diameter was used instead of the radius?
3. How does the radius change if the circumference doubles?
4. What is the relationship between area and circumference?
5. Can you express the diameter as a function of circumference?

**Tip:** Remember that the ratio of the circumference to the diameter of a circle is always \( \pi \).

The circumference *C* of a circle is a function of its radius given by *C*(r) = 2πr. a. Express the radius of a circle as a function of its circumference. Call this function r(C).

Learn how to express the radius of a circle as a function of its circumference with a detailed explanation. The problem explores the geometric relationship between radius and circumference, using the formula r(C) = C / (2π). Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation