« previous next »

Author Question: How to work out the area of a sector when i don't have the radius? (Read 1660 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?

Nearly all drugs pass into human breast milk. How often a drug is taken influences the amount of drug that will pass into the milk. Medications taken 30 to 60 minutes before breastfeeding are likely to be at peak blood levels when the baby is nursing.

Did you know?

Astigmatism is the most common vision problem. It may accompany nearsightedness or farsightedness. It is usually caused by an irregularly shaped cornea, but sometimes it is the result of an irregularly shaped lens. Either type can be corrected by eyeglasses, contact lenses, or refractive surgery.

Did you know?

When blood is deoxygenated and flowing back to the heart through the veins, it is dark reddish-blue in color. Blood in the arteries that is oxygenated and flowing out to the body is bright red. Whereas arterial blood comes out in spurts, venous blood flows.

Did you know?

On average, someone in the United States has a stroke about every 40 seconds. This is about 795,000 people per year.

Did you know?

Eating carrots will improve your eyesight. Carrots are high in vitamin A (retinol), which is essential for good vision. It can also be found in milk, cheese, egg yolks, and liver.

Striking examples where high surface area releases heat. Striking examples where high surface area releases heat.
A strike by 800 women shoemakers in Lynn, Massachusetts, in 1860. In 1851 a Lynn shoemaker had adapt A strike by 800 women shoemakers in Lynn, Massachusetts, in 1860. In 1851 a Lynn shoemaker had adapt
How to solve problems involving the area of a rectangle How to solve problems involving the area of a rectangle
Math work Math work
Trigonometry, Area Problem Trigonometry, Area Problem
An automobile engine provides 524 Joules of work to push the pistons and generates 2160 Joules ... An automobile engine provides 524 Joules of work to push the pistons and generates 2160 Joules ...
Video: Chronology of leptin research (A history of leptin research)

For a complete list of videos, visit our video library