Finding the Area of a Quarter Circle

Introduction

• Video covers finding the area of a quarter circle.
• Instructions to provide the answer to two decimal places.

Key Concepts

• Quarter Circle: A quarter of a whole circle.
• Area Formula: Area of a circle = πr²
  • For a quarter circle, divide the circle's area by 4.

Steps to Find the Area

1. Identify the Radius:
   • Given a radius (e.g., 8 cm).
2. Calculate Whole Circle's Area:
   • Use the formula: π × radius²
   • Example: π × 8² = 64π or approximately 201.06192 cm².
3. Calculate Quarter Circle's Area:
   • Divide the whole circle's area by 4.
   • Example: 64π/4 = 16π or approximately 50.26548 cm².
4. Round to Two Decimal Places:
   • Example: 50.27 cm².

Non-Calculator Example

• Given: Radius of 6 cm.
• Whole Circle's Area: π × 6² = 36π cm².
• Quarter Circle's Area: 36π/4 = 9π cm².

Solving for Radius

• Given: Area of quarter circle = 30 cm².
• Whole Circle's Area:
  • Multiply the quarter circle's area by 4: 30 × 4 = 120 cm².
• Solve for Radius Y:
  • Use formula: πy² = 120.
  • Divide by π: y² = 120/π.
  • Solve for y: y = √(120/π).
  • Example result: y ≈ 6.18 cm.

Conclusion

• To find the area of a quarter circle, calculate the full circle's area and divide by 4.
• If given the area of a quarter circle, multiply by 4 to find the full circle's area, then solve for the radius.