# 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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**Q5: **

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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**Q7: **

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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**Q8: **

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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**Q9: **

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.

**Q10: **

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

**Q11: **

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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**Q12: **

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

**Q13: **

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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**Q14: **

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

**Q16: **

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

**Q17: **

What is the length of the arc of a circle of radius that is given by of the circumference?

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**Q18: **

A circle has a central angle measuring which subtends an arc of length 21.18 cm. Find the radius of the circle giving the answer to the nearest centimeter.

**Q19: **

A circle has a radius of 14.49 cm. Find the central angle, in radians, that subtends an arc of length 8.23 cm, giving the answer to two decimal places.

**Q20: **

The perimeter of a circular sector is 19 cm and the central angle is 0.375 rad. Find the arc length giving the answer to the nearest centimetre.

**Q21: **

A circle has a radius of 1.5 cm, where the central angle subtending an arc is 1.88 rad. Find the length of the arc, giving the answer to one decimal place.

**Q23: **

A circle has a central angle measuring 1.515 rad which subtends an arc of length 25.36 cm. Find the radius of the circle to the nearest centimeter.

**Q24: **

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

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**Q25: **

The radius of a circle is 40 cm and the perimeter of a sector is 106 cm. Find the central angle in degrees giving the answer to the nearest second and in radians giving the answer to one decimal place.

- A, 0.7 rad
- B, 0.7 rad
- C, 0.3 rad
- D, 0.3 rad