# Lesson Worksheet: Arc Lengths and Sectors: Degrees Mathematics

In this worksheet, we will practice finding the arc length and the area of a sector given the angle measure in degrees.

Q1:

Given that , find the length of rounded to the nearest integer.

Q2:

What is the length of the arc subtended by a central angle of on a circle of radius ?

• A
• B
• C
• D

Q3:

An arc on a circle with a radius of 50 has a length of 115. Determine the arcβs measure to the nearest tenth of a degree.

Q4:

What angle is subtended by an arc of length 20 in a circle of circumference 80?

Q5:

An arc covers of a circleβs circumference and the circle has a radius of 78 cm. Find the measure and the length of the arc using as an approximation for , rounding the length to the nearest hundredth..

• A, 54.45 cm
• B, 108.91 cm
• C, 108.91 cm
• D, 54.45 cm

Q6:

The area of a circular sector is 815.1 cm2 and the central angle is . Find the arc length of the sector giving the answer to the nearest centimeter.

Q7:

.

Q8:

The figure shows square inscribed in a circle with center . Given that the radius of the circle with center is 32 cm, find the perimeter of the shaded region. Give your answer to the nearest centimeter.

Q9:

In the given figure, the circumference is 15 and is . Find the length of .

• A
• B
• C
• D5
• E

Q10:

Given that , determine, to the nearest whole number, the length of arc and the area of the shaded region.

• A64 cm, 480 cm2
• B32 cm, 1,320 cm2
• C129 cm, 4,441 cm2
• D32 cm, 1,800 cm2

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