The area of a circle is 25π ft². What is the circumference, in feet? Express your answer in terms of piπ.


The area \( A \) of a circle is given by the formula:

\[
A = \pi r^2
\]

Where \( r \) is the radius. You are given the area as \( 25\pi \) ft², so:

\[
25\pi = \pi r^2
\]

To find the radius, divide both sides by \( \pi \):

\[
r^2 = 25
\]

Taking the square root of both sides:

\[
r = 5 \, \text{ft}
\]

Now, to find the circumference, use the formula for the circumference of a circle:

\[
C = 2\pi r
\]

Substituting \( r = 5 \):

\[
C = 2\pi \times 5 = 10\pi \, \text{ft}
\]

So, the circumference is \( 10\pi \) feet.

Would you like any further details?

Here are 5 related questions to explore:
1. How does the area of a circle change if the radius is doubled?
2. What would the circumference be if the area were \( 100\pi \) ft²?
3. How would the radius change if the area were \( 36\pi \) ft² instead?
4. If the circumference of a circle is given, how do you find the radius?
5. How does the formula for the circumference relate to the formula for the area of a circle?

**Tip:** Remember that the area of a circle increases with the square of the radius, while the circumference increases linearly.

The area of a circle is 25π ft². What is the circumference, in feet? Express your answer in terms of π.

Learn how to find the circumference of a circle with an area of 25π ft². This step-by-step solution walks through the process of calculating the radius and then using it to find the circumference. Ideal for students in Grades 6-8 studying circle geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation