The radius of a circle is four centimeters and the perimeter of a sector is 11 centimeters. Find the arc length of the sector, giving the answer to the nearest centimeter.
First, let’s think about what a sector would look like. A sector might look something like this. And if we know the perimeter of this sector — that’s the distance all the way around — the distance all the way around is 11 centimeters. But what else can we say?
We can say that this sector is part of a circle and that two pieces of this sector are a radius of the circle. And we’ve been told that the radius of this circle is four centimeters. We can plug in four centimeters for the length of each of these lines. And the remaining length will be the arc length. That means we can say four centimeters plus four centimeters plus the arc length must equal the perimeter of the sector, 11 centimeters.
Four plus four equals eight. Eight centimeters plus the arc length must equal 11 centimeters. So we subtract eight centimeters from both sides of our equation. And the arc length must equal 11 centimeters minus eight centimeters. The arc length equals three centimeters. Four plus four plus three equals 11. Our instructions told us to give the answer to the nearest centimeter. But three centimeters is already a whole number. And so that’s our final answer.