What is the Formula for Finding the Area of a Circular Coil?

[ikentrovik]

Homework Statement

Please see attached image file

I understand everything in this problem except I don't know how they got (1/4) in the area of a coil.

Can someone explain this? I have googled it and I am not getting a clear answer.

I thought the area of a coil could be (pi(r)^2)L where l is the length. But wouldn't this be a cyclinder? How would I find it when the inner core of the cyclinder is missing?

Thank you

 

[Orodruin]

The coil is circular. The area of a circle is $\pi r^2$ and r is half of the diameter. The expression you gave is not an area, it has dimensions length^3.

 

[ikentrovik]

You are right. I guess I gace volume. What I really don't understand is why there is a (1/4). Could you please explain why? Thank you.

 

[Orodruin]

The area of a circle is $\pi r^2$ and r is half of the diameter.

r = d/2 implies r^2 = d^2/4 ...

 

[ikentrovik]

Oh ok thank you! What I did was divide the diameter in half right away. Thats why I was confused.