# Worksheet: Arc Lengths and Sectors

In this worksheet, we will practice finding the arc length, the perimeter, and the area of a circular sector using their formulas.

**Q3: **

For the given figure, is the center of the circle and is the measure of arc .

Write down an expression for the circumference of the circle.

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If is measured in degrees, what fraction of the circleβs circumference is arc ?

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Write an expression for the length of arc , given that is measured in degrees.

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**Q6: **

Write an expression for the length of an arc whose measure is radians, knowing that the expression for the length of an arc in degrees is .

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**Q8: **

An arc has a measure of radians and a radius of 6. Work out the length of the arc, giving your answer in terms of , in its simplest form.

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**Q9: **

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

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**Q10: **

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.

**Q11: **

A circle has a radius of 7.22 cm. Find the central angle that subtends an arc of length 12.53 cm, giving the answer to the nearest second.

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**Q12: **

The length of an arc in a circle is where is the radius of the circle. Find the central angle subtending the arc in radians giving the answer to one decimal place.

**Q13: **

An arc in a circle measures . What angle does it subtend?

**Q14: **

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

**Q15: **

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 , 54.45 cm
- D , 108.91 cm

**Q16: **

The length of an arc in a circle is where is the radius of the circle. Find the central angle subtending the arc in degrees giving the answer to the nearest second.

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**Q17: **

The radius of a sundial is 15 cm and the shadow changes at a rate of every hour. Find in terms of the arc length of the rotation of the shadow after 2 hours.

- A cm
- B cm
- C cm
- D cm

**Q18: **

The radius of a circle is 15 cm and the arc length of a sector is 16 cm. Find the central angle giving the answer to the nearest second.

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**Q19: **

A circle has a central angle of which subtends an arc of length cm. Find the diameter of the circle to the nearest centimeter.

**Q21: **

The area of a circular sector is 815.1 cm^{2} and the central angle is . Find the arc length of the sector giving the answer to the nearest centimeter.

**Q22: **

In the given figure, which of the following would represent the minor arc passing through and ?

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**Q23: **

Given that is a tangent to the circle , where it touches it at the point ,, and , find the length of .

**Q24: **

is a circle of radius 19 cm. Determine, to the nearest hundredth, the length of .

**Q25: **

Determine, to the nearest hundredth, the length of .