Relating circumference and area  Summary and Q&A
TL;DR
Given the circumference of a circle, you can determine the area using the formula area = circumference squared divided by four pi and vice versa.
Questions & Answers
Q: How can the area of a circle be determined if the circumference is known?
To find the area, you can use the formula area = circumference squared divided by four pi. By substituting the value of the circumference, you can calculate the area.
Q: What is the general formula that relates the circumference and area of a circle?
The formula is area = circumference squared divided by four pi. This formula allows you to find the area when only the circumference is known or vice versa.
Q: Can you explain the process of deriving the formula for relating the circumference and area?
By solving for the radius using the equation circumference = 2 pi r, and substituting it in the formula area = pi r squared, we can simplify and derive the formula area = circumference squared divided by four pi.
Q: How can the circumference be determined if the area of a circle is given?
To find the circumference, you can use the formula circumference = square root of four pi times the area. This equation allows you to calculate the circumference when the area is known.
Summary & Key Takeaways

This video discusses how to calculate the area of a circle when given its circumference and vice versa.

By using the formula 6 pi for the circumference, we can determine that the area of a circle is 9 pi square units.

The video also demonstrates how to derive a general formula that directly relates the circumference and area of a circle, which is area = circumference squared divided by four pi.