# FIND MISSING ARC AND RADIUS OF CIRCLE

To find length of arc of a sector, we will use the formula

s = rθ

Length of arc is part of the circumference of the circle, the picture clearly shows.

s = (θ/360) ∙ 2πr

Problem 1:

Find the length of arc AB.

Solution:

The formula to find the arc length is

= (Arc Measure / 360˚) ∙ 2πr

Substitute r = 6 cm, arc measure = 120˚ and π = 3.14

= (120˚/360˚) × 2 × 3.14 × 6

= 1/3 × 37.68

= 12.56 cm

So, the length of the arc is about 12.56 cm.

Problem 2:

The diameter is 24 cm. Find the length of arc CD.

Solution :

The formula to find the arc length is

= (Arc Measure / 360˚) ∙ 2πr

Diameter = 24 cm

Substitute r = 12 cm, arc measure = 60˚ and π = 3.14

= (60˚/360˚) × 2 × 3.14 × 12

= 1/6 × 75.36

= 12.56 cm

So, the length of the arc is about 12.56 cm.

Problem 3:

The length of arc EF is 5π in. find the length of the radius.

Solution :

The formula to find the arc length is

= (Arc Measure / 360˚) ∙ 2πr

Substitute length of arc = 5π in, arc measure = 30˚ and π = 3.14

5π = (30˚/360˚) × 2 × π × r

5π = 1/6 × π × r

r = 30 in

Problem 4:

Find the length of arc XY.

Solution :

The formula to find the arc length is

= (Arc Measure / 360˚) ∙ 2πr

Substitute r = 10 cm, arc measure = 70˚ and π = 3.14

= (70˚/360˚) × 2 × 3.14 × 10

= 12.21 cm

So, the length of the arc is about 12.21 cm.

Problem 5 :

A circle has an arc whose measure is 80˚ and whose length is 88π. What is the diameter of the circle?

Solution :

The formula to find the arc length is

= (Arc Measure / 360˚) ∙ 2πr

Substitute length of arc = 88π, arc measure = 80˚ and π = 3.14

88π = (80˚/360˚) × 2 × π × r

88π = 4/9 × π × r

r = 198

Diameter = 2 × 198

Diameter = 396

So, diameter of the circle is 396.

Problem 6 :

A circle has a circumference whose length is 25π. Find the length of an arc whose central angle is 90˚.

Solution :

The formula to find the arc length is

= (Arc Measure / 360˚) ∙ 2πr

Substitute circumference = 25π, arc measure = 90˚

= (90˚/360˚) × 25π

= 1/4 × 25π

= 6.25π

So, length of an arc is 6.25π.

Problem 7 :

Find the measure of the central angle of an arc if its length is 14π and the radius is 18.

Solution :

Arc length = 14π and radius = 18

The formula to find the arc length is

14 π = (Arc Measure / 360˚) ∙ 2πr

14 π = (Arc Measure / 360˚) ∙ 2 × π × 18

Arc measure = (14π × 360)/2 × π × 18

= 140˚

So, measure of the central angle of an arc is 140˚.

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