# Worksheet: Arc Length

Q1:

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.

Q2:

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

Q3:

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

Q4:

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.

• A
• B
• C
• D
• E

Q5:

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.

• A
• B
• C
• D
• E

Q6:

A circle has a radius of 7.19 cm. Find the central angle that subtends an arc of length 11.21 cm, giving the answer to the nearest second.

• A
• B
• C
• D
• E

Q7:

An arc covers of a circleβs circumference and the circle has a radius of 78 cm. Find, to the nearest hundredth, the measure and the length of the arc, using as an approximation for .

• A , 54.45 cm
• B , 108.91 cm
• C , 54.45 cm
• D , 108.91 cm

Q8:

The radius of a sundial is 35 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 10 hours.

• A cm
• B cm
• C cm
• D cm

Q9:

The radius of a sundial is 26 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 4 hours.

• A cm
• B cm
• C cm
• D cm

Q10:

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.

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.

• A
• B
• C
• D

Q12:

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

• A 11 cm
• B 44 cm
• C 28 cm
• D 22 cm

Q13:

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

• A
• B
• C
• D
• E

Q14:

Calculate the length of an arc on Earthβs surface that subtends an angle of 7 minutes at Earthβs center knowing that of a degree. Take Earthβs radius to be miles.

Q15:

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

Q16:

In the given figure, the circumference is 15 and is . Find the length of .

• A
• B 5
• C
• D
• E

Q17:

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

Q18:

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

Q19:

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.

• A
• B
• C
• D

Q20:

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.

• A
• B
• C
• D
• E

If is measured in degrees, what fraction of the circleβs circumference is arc ?

• A
• B
• C
• D
• E

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

• A
• B
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• D
• E

Q21:

Given that , find the length of rounded to the nearest integer.

Q22:

The area of a circular sector is 815.1 cm2 and the central angle is . Find the arc length of the sector giving the answer to the nearest centimeter.

• A 84 cm
• B 39 cm
• C 3 cm
• D 42 cm

Q23:

Determine, to the nearest hundredth, the length of .

Q24:

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

Q25:

.