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Mathematics Clinic => Grade 9 Mathematics => Topic started by: TI on Oct 4, 2013

Title: How to work out the area of a sector when i don't have the radius?
Post by: TI on Oct 4, 2013

i have to find the area of a sector but i have been given only the angle(40degrees) and the arc length(18cm) how do i work it out? I suck at rearranging the formula so i would appreciate if you could show me. thnx

Title: How to work out the area of a sector when i don't have the radius?
Post by: formula1 on Oct 4, 2013

To find the Area of Circle Sector: (with central angle theta)>if the angle theta is in degrees, then area = (theta/360) PI r2>if the angle theta is in radians, then area = (theta/2) r2

good luck

Title: How to work out the area of a sector when i don't have the radius?
Post by: sadsdas on Oct 4, 2013

You know the circumference of a circle is pi times twice the radius.

There are 360 degrees in a circle.

So 40/360 = 18/circumference.

Circumference = 162

Therefore, radius = 81/pi

Area of the circle = pi (81/pi)^2 = 6561/pi

So the area of the sector = (6561/pi) * (40/360) = 729/pi

Which is approximately 232 square centimeters.

Title: How to work out the area of a sector when i don't have the radius?
Post by: xclash on Oct 4, 2013

There are 360 degrees in a circle so 40 degrees has to by 40/360 or 1/0 the actual size of the circle:

Perimeter = 2 * pi * r
18cm = 2 * 1/9 * pi * r
r = 81 / pi

area = pi * r^2
area = pi * (81 / pi)^2 * 40/360

Title: How to work out the area of a sector when i don't have the radius?
Post by: sadsdas on Oct 4, 2013

to get the radius there is a rule that says r=lenght of arc/angle in rad
so u got convert the 40 degrees into rad 40*pie/180 =2/9pie(rad) ,pie=3.14
so the r=length of arc 18cm divided by 2/9pie = 25.78cm !

so area = 1/2 L*R
              1/2 18 *25.78=232