# 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.

**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 cm
^{2} - B cm
^{2} - C cm
^{2} - D cm
^{2}

**Q4: **

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

**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 circleβs 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 circleβs 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 circleβs 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.

**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 cm^{2} 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 arcβs measure to the nearest tenth of a degree.

**Q19: **

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

**Q22: **

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

- A
- B rad
- C
- D
- E rad

**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

**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