Video: Finding the Equation for the Area of a Sector When the Angle Is Given in Degrees

The circle in the given figure has a radius π‘Ÿ, and the angle of the sector is πœƒ. Write down an expression for the area of the circle. What fraction of the circle is the sector with central angle πœƒ? Write an expression for the area of the sector.

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Video Transcript

The circle in the given figure has a radius π‘Ÿ, and the angle of the sector is πœƒ. Write down an expression for the area of the circle. What fraction of the circle is the sector with central angle πœƒ? Write an expression for the area of the sector.

We know that the expression for the area of a circle with radius π‘Ÿ is πœ‹π‘Ÿ squared. And we know that angles around a point sum to 360 degrees. To find the fraction of the circle a sector with central angle πœƒ is, we’re going to divide πœƒ by 360. It’s πœƒ over 360.

Finally, we need to find an expression for the area of the sector. The fraction of the circle the sector is, is πœƒ over 360. So we need to find πœƒ over 360ths [360] of the total area of πœ‹π‘Ÿ squared. In maths, we commonly interchange β€œof” and the multiplication symbol.

So the expression for the area of the sector with central angle πœƒ is πœƒ over 360 multiplied by πœ‹π‘Ÿ squared.

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