# Lesson Worksheet: Arc Lengths Mathematics • 10th Grade

In this worksheet, we will practice finding the arc length and the perimeter of a circular sector using radians and solve problems including real-life situations.

Q1:

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.

• A
• B
• C
• D
• E

Q2:

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.

• A cm
• B cm
• C cm
• D cm
• E cm

Q3:

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

Q4:

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

• A
• B
• C
• D
• E

Q5:

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.

Q6:

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 .

• A
• B
• C
• D
• E

Q7:

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.

Q8:

Find the perimeter of in the following diagram.

Q9:

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.

Q10:

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.