# 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.

Q1:

Find the length of the blue arc given the radius of the circle is 8 cm. Give the answer to one decimal place. Q2:

An arc has a measure of radians and a radius of 9. Work out the length of the arc, giving your answer in terms of , in its simplest form.

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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 circle’s 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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Q4:

Circle has a radius of 12 cm where the length of is 16 cm. Find the length of arc giving the answer to two decimal places. 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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Q6:

If and the radius of the circle equals 3 cm, find the length of the major arc . 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.

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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.

Q15:

Calculate the length of an arc on Earth’s surface that subtends an angle of 7 minutes at Earth’s center knowing that of a degree. Take Earth’s radius to be 3,960 miles.

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.

Q22:

Calculate the length of an arc on Earth’s surface that subtends an angle of 5 minutes at Earth’s center, knowing that 1 minute is equal to of a degree. Take the Earth’s radius to be 3,960 miles.

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 arc’s 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.