Q308a, Arc length and Area of Sector of a circle | Summary and Q&A

TL;DR

The content explains how to calculate the arc length and area of a sector of a circle using both degrees and radians.

Key Insights

• 🫠 The length of an arc is a portion of the circumference of a circle.
• 🫠 The formula for calculating the length of an arc depends on whether the angle is given in degrees or radians.
• ⭕ The area of a sector is a portion of the whole area of a circle.
• ⚾ The formula for finding the area of a sector also varies based on whether the angle is in degrees or radians.

Transcript

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Questions & Answers

Q: What is the formula for calculating the length of an arc?

The length of an arc can be calculated using the formula (θ/360) x 2πr, where θ is the angle of the arc in degrees and r is the radius of the circle.

Q: How do you calculate the length of an arc if the angle is given in radians?

If the angle is given in radians, the formula becomes just rθ, where r is the radius and θ is the angle in radians.

Q: What is the formula for finding the area of a sector using degrees?

To find the area of a sector in degrees, you can use the formula (θ/360) x πr², where θ is the angle of the sector and r is the radius of the circle.

Q: How do you calculate the area of a sector if the angle is given in radians?

If the angle is given in radians, the formula for finding the area of a sector is (θ/2) x r², where θ is the angle in radians and r is the radius of the circle.

Summary & Key Takeaways

• The length of an arc on a circle is a portion of the circumference, which can be calculated using the formula (θ/360) x 2πr.

• To find the area of a sector, you need to know the whole area of the circle and the angle of the sector. The formula is (θ/360) x πr².