Find the area of a sector of a circle intercepted by a central angle of 150 degree in a circle of radius 5.3cm

Answer 1

To solve this, we can take a ratio of the circle as a whole.

Knowing the radius of the circle is 5.3cm and the area of a circle is pi*r²

(3.14159)(5.3²) = 88.2473cm² = Area_{Whole Circle}

Now we need the ratio of the sector to the whole circle.

We know the angle of the sector is 150 degrees and a circle has 360 degrees.

Setting up a proportion:

Sector / Whole = 150 degrees / 360 degrees = A_Sector / A_Whole = A_Sector / 88.2473 cm²

150 degrees * 88.2473 cm² = 360 degrees * A_Sector

150 degrees * 88.2473 cm²

------------------------------------ = A_Sector

360 degrees

A_Sector = 36.77 cm²