Find the area of a sector with the given central angle Theta in radius r:
Theta= 2(in radians) and r = 10 inches
Very confused how they got 100 sq inches

Question

Find the area of a sector with the given central angle Theta in radius r:
Theta= 2(in radians) and r = 10 inches 
Very confused how they got 100 sq inches

anonymous · Answer

step by step please

anonymous · Answer

We know:$$A _{sector}=(1/2)r^2\theta$$
Keep in mind that theta in this case must be in radians, not degrees.
So,$$A _{sector}=(1/2)10^2(2)$$$$A _{sector}=(1/2)200$$
$$A _{sector}=100in^2$$

anonymous · Answer

I can't find that formula in my book  hmm... and it says it falls under the category of arc length, linear and angular velocity chapter. (This is a trig class). any way of doing that with s=r*theta or v= s/t or w= theta/t? or is it far more basic than that?

anonymous · Answer

What is s, v, and w in those formulas?

anonymous · Answer

Also "t"

anonymous · Answer

arc length linear velocity and angular velocity

anonymous · Answer

t is just a length on the unit circle

anonymous · Answer

can you just explain to me the forumla a little like where you got 1/2 what r^2 represent etc

anonymous · Answer

hm, I've never seen sector area calculated via kinematics. Deriving a formula for sector area from those 3 equations seems very difficult since none of them have an area variable in them. I remember the basic formula for the area of a sector is$$A _{sector}=(1/2)r^2\theta$$Where r is the radius and theta is the angle of the sector.

anonymous · Answer

No need for all this complication.

The area of the circle is pi r^2 ie a 100 pi

Your piece of it is 2/2pi  = 1/pi radians (there are 2pi radians in the whole circle) SO

100 pi + 1/pi = 100

That's it.

anonymous · Answer

100 pi * 1/pi = 100 (not +)