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.

Key Insights

• 🤨 The area of a circle can be determined if the circumference is known by using the formula area = circumference squared divided by four pi.
• 🤨 The general formula for relating circumference and area is area = circumference squared divided by four pi.
• 👏 To calculate the circumference when the area is given, you can use the formula circumference = square root of four pi times the area.

Transcript

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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.