# Question Video: Finding the Area of a Circular Sector given Its Circle Radius Length and Its Central Angle Mathematics

The radius of a circle is 21 cm and the angle of a sector is 123Β°. Find the area of the sector giving the answer to the nearest square centimeter.

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### Video Transcript

The radius of a circle is 21 centimeters, and the angle of a sector is 123 degrees. Find the area of the sector, giving the answer to the nearest square centimeter.

A sector is part of a circle enclosed by two radii and part of the circle circumference, which we call an arc. The sector in this question has a radius of 21 centimeters and a central angle of 123 degrees. Thatβs the angle where the two radii meet at the center of the circle. Weβre asked to find the area of this sector. So letβs recall the formula for doing so. The area of a sector with a radius of π units and a central angle of π degrees is given by π over 360 multiplied by ππ squared. Practically, we can see where this formula comes from. ππ squared gives the area of the full circle, and then we multiply this by π over 360, which is the fraction of the full circle represented by the sector.

As we know the values of π, the radius of the circle, and π, the central angle, we can substitute these into the formula to calculate the area of the sector. It gives 123 over 360 multiplied by π multiplied by 21 squared. That simplifies to 54,243 over 360 multiplied by π. Weβre asked to give our answer to the nearest square centimeter, so we need to evaluate this as a decimal. That gives 473.359 continuing. We then need to round this answer to the nearest integer, which is 473. The area of a sector with a radius of 21 centimeters and a central angle of 123 degrees to the nearest square centimeter is 473 square centimeters.