Lesson: Arc Lengths Mathematics

In this lesson, we will learn how to find the arc length and the perimeter of a circular sector using radians and solve problems including real-life situations.

Lesson Plan

Students will be able to

recognize the formulas for calculating arc length when the measure of the arc is given in radians,
calculate the length of a sector’s arc,
calculate the measure of the angle of a sector in radians when given the radius and arc length of the arc,
calculate the radius of a sector when given the measure of the arc in radians and the length of the arc (or perimeter),
calculate the perimeter of a sector,
solve real-world problems by finding arc lengths.

Lesson Worksheet

Q1:

An arc of a circle has a length of 2.7 cm and it subtends an angle of 0.3 rad. Find the radius of the circle.

Q2:

An arc of a circle of radius cm subtends an angle of rad. Given that the perimeter of this sector is cm, find an expression for in terms of and .

Q3:

Find the length of the arc of a circle of radius 3.1 cm that subtends an angle of 1.1 rad.