Video: Finding the Perimeter of a Circular Sector given Its Central Angle and the Circle’s Radius

The radius of a circle is 7 cm and the central angle of a sector is 40°. Find the perimeter of the sector to the nearest centimeter.

02:21

Video Transcript

The radius of a circle is seven centimeters and the central angle of a sector is 40 degrees. Find the perimeter of the sector to the nearest centimeter.

First, we want to just sketch our circle and then label each part. We have a radius of seven centimeters. One of the sectors measures 40 degrees. We’re looking for the perimeter of this sector. We know that the perimeter would be the distance all the way around. The distance all the way around the sector — the perimeter of a sector — would be equal to the radius plus the radius plus the arc length of that sector.

We already know what the radius is. So we’ll need to calculate the arc length in order to calculate the perimeter. There’s a formula for finding arc length. Arc length is equal to 𝜃 times the radius. However, this formula assumes that 𝜃 the angle measure is measured in radians.

We’re given a central angle measured in degrees. And that means we’ll have to modify the formula. We need to multiply 𝜋 over 180 degrees times our angle measure times the radius. Our arc length equals 𝜋 over 180 degrees times 40 degrees times seven. When we multiply that together, we get 4.88 of a centimeter. We want to round to the nearest centimeter. 4.8 rounded to the nearest whole number is five. Our arc length is about five centimeters.

We plug that five centimeters in for the arc length. And now, we have the perimeter is equal to seven plus seven plus five.

The perimeter the distance all the way around this sector is equal to 19 centimeters.

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