« previous next »

Author Question: How to work out the area of a sector when i don't have the radius? (Read 1612 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?

When intravenous medications are involved in adverse drug events, their harmful effects may occur more rapidly, and be more severe than errors with oral medications. This is due to the direct administration into the bloodstream.

Did you know?

As of mid-2016, 18.2 million people were receiving advanced retroviral therapy (ART) worldwide. This represents between 43–50% of the 34–39.8 million people living with HIV.

Did you know?

All patients with hyperparathyroidism will develop osteoporosis. The parathyroid glands maintain blood calcium within the normal range. All patients with this disease will continue to lose calcium from their bones every day, and there is no way to prevent the development of osteoporosis as a result.

Did you know?

All adults should have their cholesterol levels checked once every 5 years. During 2009–2010, 69.4% of Americans age 20 and older reported having their cholesterol checked within the last five years.

Did you know?

Acetaminophen (Tylenol) in overdose can seriously damage the liver. It should never be taken by people who use alcohol heavily; it can result in severe liver damage and even a condition requiring a liver transplant.

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
Locations of Broca’s Area, Wernicke’s Area, and Associated Areas Involved in Language Deficits Locations of Broca’s Area, Wernicke’s Area, and Associated Areas Involved in Language Deficits
Effleurage with palms to reconnect the hip area to the leg. Slide the palms from foot to around the ... Effleurage with palms to reconnect the hip area to the leg. Slide the palms from foot to around the ...
A container in the shape of a right circular cylinder with no top has surface area square feet. A container in the shape of a right circular cylinder with no top has surface area square feet.
If the particle moves in a circle of radius 0.15 m at a speed of 3.0 m/s, what is the magnitude ... If the particle moves in a circle of radius 0.15 m at a speed of 3.0 m/s, what is the magnitude ...
Video: What is Cholesterols? Introduction to Lipoproteins

For a complete list of videos, visit our video library