Finding the Area of a Sector
When you need to find the area of a sector (a "pizza slice" of a circle), there's a simple three-step process to follow. Think of it as figuring out what fraction of the whole pizza you're getting!
First, calculate the area of the entire circle using the formula π × r². For example, with a circle of radius 5 cm, the area would be π × 5² = 78.5 square cm. This gives you the total "pizza" area.
Second, determine what fraction of the circle your sector represents by dividing the arc measure by 360°. In our example problem with a 120° sector, the fraction would be 120/360 = 1/3, meaning our sector is one-third of the circle.
Finally, multiply the circle's area by your fraction to find the sector area. For our example: 78.5 × 1/3 ≈ 26.17 square cm. That's it! You've found the area of your sector.
Try This! Imagine a circle with radius 8 cm and a sector with angle 90°. Before calculating, can you estimate what fraction of the circle this sector represents?
