An arc measure is the measure of an angle that the arc creates at the center of the circle. This measure can be given in degrees.

Arc length of a sector is the length of the portion on the circumference of the circle intercepted between the bounding radii and is denoted by l.

Formula to find the length of the arc l is

** l = (θ/360) x 2**π**r**

To solve for arc measure, we have to solve θ in the above formula.

**Example 1 :**

The radius of a sector is 42 cm and its sector angle is 60°. Find its arc length

**Solution :**

**Radius of the sector = 42 cm**

**Sector angle **θ = 60°

Length of the arc is

l = (θ/360) x 2Πr

= (60°/360°) x 2 x (22/7) x 42

= (1/6) x 2 x 22 x 6

= 44 cm

**Example 2 :**

The arc length of a sector is 66 cm and the central angle is 30°. Find its radius.

**Solution :**

**Arc length of sector = 66 cm**

**Sector angle **θ = 30°

Formula for length of the arc is

l = (θ/360) x 2Πr

Substitute the known values and solve for r.

66 = (30°/360°) x 2 x (22/7) x r

66 = (1/12) x 2 x 22 x r

r = (66 x 12)/(2 x 22)

r = 126 cm

**Example 3 :**

The length of arc of a sector is 22 cm and its radius is 10.5 cm. Find its central angle.

**Solution :**

**Arc length of sector = 22 cm**

**radius = 10.5 cm **

Formula for length of the arc is

l = (θ/360°) x 2Πr

Substitute the known values and solve for θ.

22 = (θ/360) x 2 x (22/7) x 10.5

22 = (θ/360) x 2 x 22 x 1.5

θ = (22 x 360)/(2 x 22 x 1.5)

= 180/1.5

θ = 120°

**Example 4 :**

A pendulum swings through an angle of 30° and describes an arc length of 11 cm. Find the length of the pendulum.

**Solution :**

**Arc length of sector = 11 cm**

**sector angle = 30**°

If the pendulum swings once, then it forms a sector and the radius of the sector is the length of the pendulum.

So,

l = (θ/360°) x 2Πr

Substitute the known values and solve for r.

11 = (30°/360°) x 2 x (22/7) x r

11 = (1/12) x 2 x (22/7) x r

r = (11 x 7 x 12)/(2 x 22)

r = 7 x 3

r = 21 cm

So, the length of pendulum is 21 cm

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**