« previous next »

Author Question: How to work out the area of a sector when i don't have the radius? (Read 1638 times)

TI

  • Sr. Member
  • ****
  • Posts: 434
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


formula1

  • Hero Member
  • *****
  • Posts: 666
Reply #1 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


Related Topics

Need homework help now?

Ask unlimited questions for free

Ask a Question

sadsdas

  • Newbie
  • *
  • Posts: 10
Reply #2 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.


xclash

  • Hero Member
  • *****
  • Posts: 681
Reply #3 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


sadsdas

  • Newbie
  • *
  • Posts: 10
Reply #4 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


« previous next »
 

Did you know?

Drug abusers experience the following scenario: The pleasure given by their drug (or drugs) of choice is so strong that it is difficult to eradicate even after years of staying away from the substances involved. Certain triggers may cause a drug abuser to relapse. Research shows that long-term drug abuse results in significant changes in brain function that persist long after an individual stops using drugs. It is most important to realize that the same is true of not just illegal substances but alcohol and tobacco as well.

Did you know?

Elderly adults are living longer, and causes of death are shifting. At the same time, autopsy rates are at or near their lowest in history.

Did you know?

There are approximately 3 million unintended pregnancies in the United States each year.

Did you know?

The term bacteria was devised in the 19th century by German biologist Ferdinand Cohn. He based it on the Greek word "bakterion" meaning a small rod or staff. Cohn is considered to be the father of modern bacteriology.

Did you know?

Approximately 500,000 babies are born each year in the United States to teenage mothers.

Clear the popliteal catchment area. Stand next to the recipient’s knee, and face the head of the ... Clear the popliteal catchment area. Stand next to the recipient’s knee, and face the head of the ...
Breast-Feeding at Work Can Work Breast-Feeding at Work Can Work
A 2.10-kg hammer is transported to the Moon. The radius of the Moon is 1.74 × 106 m, its mass ... A 2.10-kg hammer is transported to the Moon. The radius of the Moon is 1.74 × 106 m, its mass ...
What is the maximum velocity (in km/s) of a photoelectron emitted from a surface whose work ... What is the maximum velocity (in km/s) of a photoelectron emitted from a surface whose work ...
Calculating the area of a circular ring Calculating the area of a circular ring
The forces of diffusion and electrostatic pressure. (a) In diffusion, solutes move from an area of h The forces of diffusion and electrostatic pressure. (a) In diffusion, solutes move from an area of h
Video: Conjunctivitis

For a complete list of videos, visit our video library