Lesson Worksheet: Arc Lengths Mathematics • 10th Grade

An arc has a measure of radians and a radius of 9. Work out the length of the arc, giving your answer in terms of , in its simplest form.

The diagram shows a sector of a circle of radius cm and central angle rad.

Find the length of the arc of the sector, giving your answer exactly.

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

An arc on a circle with a radius of 12 has a length of 14. Determine the arc’s measure, giving your answer in radians as a fraction in its simplest form.

An arc of a circle of radius 5 cm has a length of 3.5 cm. Find the angle subtended by the arc in radians.

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 .

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.

Find the perimeter of in the following diagram.

The shape of the base of a bottle consists of a line segment of length 5 cm that is connected to the arc of a circle of radius 3 cm as shown.

Find the length of the arc of the circle to one decimal place.

During a soccer game, a free kick is awarded at a point that is 25 yd away from the left goalpost, as shown in the diagram. The rules state that when a free kick takes place, the players of the opposing team must stand at least 10 yd away from the ball, that is, behind the circular arc .

Point is where the ball lies, points and mark the edges of the goal, and points and mark the points on and that are 10 yd away from .

Given that the goalmouth is 8 yd wide, calculate the perimeter of the shaded area . Give your answer to the nearest yard.