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

• [Instructor] So we have a circle here, let's say that we know that its circumference is equal to six pi, I'll write it, units. Whatever our units happen to be. Let's see if we can figure out, given that its circumference is 6 pi of these units, what is the area going to be equal to? Pause this video and see if you can figure it out on your own. A... Read More

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.