Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

In this lesson, we will learn how to find the length of an arc subtended by a given central angle and how to find the central angle subtended by a given arc.

Q1:

Circle π has a radius of 12 cm where the length of πΆ π΅ is 16 cm. Find the length of arc πΆ π΅ 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 π β π΄ = 7 6 β and the radius of the circle equals 3 cm, find the length of the major arc π΅ πΆ .

Q4:

An arc has a measure of 2 π 3 radians and a radius of 9. Work out the length of the arc, giving your answer in terms of π , in its simplest form.

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.

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.

Q7:

An arc covers 2 9 of a circleβs circumference and the circle has a radius of 78 cm. Find, to the nearest hundredth, the measure and the length of the arc, using 2 2 7 as an approximation for π .

Q8:

The radius of a sundial is 35 cm and the shadow changes at a rate of 1 5 β every hour. Find in terms of π the arc length of the rotation of the shadow after 10 hours.

Q9:

The radius of a sundial is 26 cm and the shadow changes at a rate of 1 5 β every hour. Find in terms of π the arc length of the rotation of the shadow after 4 hours.

Q10:

The length of an arc in a circle is 1 . 2 π where π 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 2 π where π is the radius of the circle. Find the central angle subtending the arc in degrees giving the answer to the nearest second.

Q12:

A circle has a central angle of 6 4 5 4 β² 5 8 β² β² β which subtends an arc of length 4 π cm. Find the diameter of the circle to the nearest centimetre.

Q13:

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

Q14:

Calculate the length of an arc on Earthβs surface that subtends an angle of 7 minutes at Earthβs centre knowing that 1 = 1 6 0 m i n u t e d e g r e e s of a degree. Take Earthβs radius to be 3β960 miles.

Q15:

An arc in a circle measures 1 6 π π . What angle does it subtend?

Q16:

In the given figure, the circumference is 15 and π β π΄ π π΅ is 6 0 β . Find the length of π΄ π΅ .

Q17:

Given that β ο© ο© ο© ο© β π΄ πΆ is a tangent to the circle π , where it touches it at the point π΄ , π΅ π = 3 6 c m , and π΄ πΆ = 5 4 c m , find the length of π΄ π· .

Q18:

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

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.

Q20:

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

Write down an expression for the circumference of the circle.

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

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

Q21:

Given that π΄ π = 1 1 c m , find the length of π΄ π΅ πΆ rounded to the nearest integer.

Q22:

The area of a circular sector is 815.1 cm^{2} and the central angle is 6 2 β . Find the arc length of the sector giving the answer to the nearest centimetre.

Q23:

Determine, to the nearest hundredth, the length of π π .

Q24:

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

Q25:

l e n g t h o f t h e a r c c i r c u m f e r e n c e o f t h e c i r c l e m e a s u r e o f t h e a r c = β― .

Donβt have an account? Sign Up