# 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, and the angle of the sector is π. Write down an expression for the area of the circle. What fraction of the circle is the sector with central angle π? 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, and the angle of the sector is π. Write down an expression for the area of the circle. What fraction of the circle is the sector with central angle π? Write an expression for the area of the sector.

We know that the expression for the area of a circle with radius π is ππ 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 is, weβre going to divide π by 360. Itβs π 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 over 360. So we need to find π over 360ths [360] of the total area of ππ squared. In maths, we commonly interchange βofβ and the multiplication symbol.

So the expression for the area of the sector with central angle π is π over 360 multiplied by ππ squared.