# Worksheet: Arc Lengths and Sectors: Degrees

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

Q1:

The radius of a circle is 28 cm and the arc length of a sector is 37 cm. Find the area of the sector.

Q2:

The radius of a circle is 12 cm and the angle of a sector is . Find the area of the sector giving the answer in terms of .

• A cm2
• B cm2
• C cm2
• D cm2

Q3:

A circular birthday cake with a diameter of 22 cm is divided into eleven equal sectors. Using 3.14 as an approximation for , find the area of one sector.

Q4:

The length of an arc in a circle is of the circle’s circumference. Find the central angle subtending the arc giving the answer correct to the nearest degree.

Q5:

Shown is a sector of a circle. If its perimeter is 39 mm, what is its area? Q6:

An arc has a measure of and a radius of 4.5. Work out the area of the sector, in terms of , in its simplest form.

• A
• B
• C
• D
• E

Q7:

Circle has a diameter of length 36 cm where . Find the length of the minor arc in centimetres giving the answer to two decimal places. Q8:

A squash player moves in an arc-shaped path in a circle of radius 1.6 meters with a rotation angle of . Find the length of the arc that the player makes giving the answer to one decimal place.

Q9:

is a right-angled triangle at drawn inside a circle dividing the circle into three arcs where and . Find the lengths of the circle’s three minor arcs giving the answers to one decimal place.

• Aarc , arc , arc
• Barc , arc , arc
• Carc , arc , arc
• Darc , arc , arc

Q10:

An arc covers of a circle’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

Q11:

A circle has a radius of 5 cm and passes through the vertices of triangle where and . Find the lengths of the circle’s three minor arcs giving the answers to one decimal place.

• A, ,
• B, ,
• C, ,
• D, ,

Q12:

and are two tangents to the circle where . Find the length of the major arc giving the answer to the nearest centimetre. Q13:

is a right triangle at with an area of 58 cm2. Find the perimeter of the colored part of the figure giving the answer to two decimal places. Q14:

The arc length of a sector is 49 cm where the central angle is . Find the perimeter of the circle giving the answer to the nearest centimeter.

Q15:

The area of a circle is 160 cm2 and a central angle of a sector is . Find the area of the sector giving the answer to two decimal places.

Q16:

The radius of a circle is 16 cm and the angle of a sector is . Find the area of the sector giving the answer to the nearest square centimeter.

Q17:

Find the circumference of the circular sector whose arc length is 12 cm and angle is .

• A9 cm
• B72 cm
• C18 cm
• D36 cm

Q18:

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

Q19:

Determine, to the nearest tenth, the area of the shaded part in the given figure. Q20:

An arc has a measure of and a radius of 4.

Work out the length of the arc. Give your answer in terms of and in its simplest form.

• A
• B
• C
• D
• E

Work out the area of the sector. Give your answer in terms of and in its simplest form.

• A
• B
• C
• D
• E288

Q21:

In this figure, the diameter of the larger circle is 41 cm and both circles have the same center. Determine, to the nearest tenth, the area of the shaded part. Q22:

What is the formula for the perimeter of a sector with radius and arc length ?

• A
• C
• D

Q23:

An arc has a measure of and a radius of 8. Calculate the length of the arc, in terms of , in its simplest form.

• A
• B
• C
• D
• E

Q24:

Find the area of the shaded part in the figure. Round your answer to the nearest tenth. Q25:

What is the definition of a circular sector?

• Athe region of a circle bounded by an arc and a chord passing by the ends of this arc
• Bthe region of a circle bounded by two radii and a chord
• Ca part of the circumference between two points or a continuous piece of a circle
• Dthe region of a circle bounded by two radii and an arc
• Ean arc which is half of the circumference