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

Video Transcript

The circle in the given figure has a radius 𝑟, and the angle of the sector is 𝜃. Write down an expression for the area of the circle. What fraction of the circle is the sector with central angle 𝜃? Write an expression for the area of the sector.

We know that the expression for the area of a circle with radius 𝑟 is 𝜋𝑟 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 𝜃 is, we’re going to divide 𝜃 by 360. It’s 𝜃 over 360.

Finally, we need to find an expression for the area of the sector. The fraction of the circle the sector is, is 𝜃 over 360. So we need to find 𝜃 over 360 of the total area of 𝜋𝑟 squared. In maths, we commonly interchange “of” and the multiplication symbol.

So the expression for the area of the sector with central angle 𝜃 is 𝜃 over 360 multiplied by 𝜋𝑟 squared.