# ARC MEASURE AND ARC LENGTH

## About "Arc measure and arc length"

Arc measure and arc length :

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

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

Length of arc = (θ/360) x 2Πr

## Arc measure and arc length - Examples

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°

To find the arc length, we need to use the formula

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°

l  =  (θ/360) x 2Πr

Applying the values of arc length and central angle in the formula, we get

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)

=  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

l  =  (θ/360) x 2Πr

Applying the values of arc length and central angle in the formula, we get

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°

Hence the required central angle is 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

Applying the values of arc length and central angle in the formula, we get

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

Hence the length of pendulum is 21 cm

After having gone through the stuff given above, we hope that the students would have understood "Arc measure and arc length".

Apart from the stuff given above, if you want to know more about "Arc measure and arc length", please click here

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

You can also visit our 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

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6