Question

49. If the sector formed by a central angle of 30 degrees has an area of pi/3 square centimeters, find the radius of the circle.

MY REAL PROBLEM: What is the length of the arc cut off by angle (theta) in problem 49?

Answer 1

Remember the pi/4 problem from before? Reasoning is the same: 30(pi/6 rad) is 1/12th of the whole circle. It means the surface is 12pi/3 = 4pi. it means radius is sqrt(4pi/pi) = 2, and the circle lenght is 2*pi*2 = 4pi. Since you need only 1/12th you get that your arc measures (4/12)pi

Answer 2

How do you kno0w that 30(pi/6rad) is 1/12 of the whole circle? I dont understand?

Answer 3

the whole circle is 360°. 30:360 = 1:12. Once you understand what part of the whole you're dealing with you just have to multiply by it.

Answer 4

How did you get 12pi/3? UGH sorry Im just so confused!

Answer 5

You understand how your angle is 1/12th of the whole circle? If one part is pi/3, then the whole of it is 12 times that: 12 * pi/3

Answer 6

You said you only need 1/12 of 4pi? How did you get that ?

Answer 7

4pi is the WHOLE circle, your problem asked only the part of it, which still is that 1/12

Answer 8

...uh okay. so What is that the answer to 49? lol. Do i need to know the answer to 49 to get 50. Thats what Im trying to do it get 50.

Answer 9

Radius of the circle? It's 2 (explanation is in my first post)