« previous next »

Author Question: How to work out the area of a sector when i don't have the radius? (Read 3764 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?

Most strokes are caused when blood clots move to a blood vessel in the brain and block blood flow to that area. Thrombolytic therapy can be used to dissolve the clot quickly. If given within 3 hours of the first stroke symptoms, this therapy can help limit stroke damage and disability.

Did you know?

More than 34,000 trademarked medication names and more than 10,000 generic medication names are in use in the United States.

Did you know?

A recent study has found that following a diet rich in berries may slow down the aging process of the brain. This diet apparently helps to keep dopamine levels much higher than are seen in normal individuals who do not eat berries as a regular part of their diet as they enter their later years.

Did you know?

In 1835 it was discovered that a disease of silkworms known as muscardine could be transferred from one silkworm to another, and was caused by a fungus.

Did you know?

Automated pill dispensing systems have alarms to alert patients when the correct dosing time has arrived. Most systems work with many varieties of medications, so patients who are taking a variety of drugs can still be in control of their dose regimen.

The Cardiac Landmarks. A = Aortic Area; P = Pulmonic Area; E = Erb’s Point; T = Tri The Cardiac Landmarks. A = Aortic Area; P = Pulmonic Area; E = Erb’s Point; T = Tri
Einstein - Science is the work of... Einstein - Science is the work of...
Broca’s Area Broca’s Area
How Self-Fulfilling Stereotypes Work. How Self-Fulfilling Stereotypes Work.
Apply superficial friction with the towel to warm and dry the area. Apply superficial friction with the towel to warm and dry the area.
The European Alps have lost ~30% to 40% of surface area and ~50% of volume since the 1850s. The European Alps have lost ~30% to 40% of surface area and ~50% of volume since the 1850s.
Video: Mycobacterium tuberculosis: Drug Resistance and Natural Selection

For a complete list of videos, visit our video library