Find the circumference in terms of r

Question

I've managed to work out that the length $AB$ is $\sqrt{3} r$

I'm getting completely different answers from the correct one for part b of the question: $\sqrt{3}\pi r$

I'm not even $100%$ sure if it is referring to the circumference of the major or minor segment. I've tried to work out both and still don't get that answer. Any tips?

Cheers!!

Answer 1

I think you are misunderstanding the wording of the problem. Once you find the length AB you can very easily use the formula $\pi\times \mbox{diameter}$ to find the circumference the question refers to. The diameter is the length AB; simply multiply it by $\pi$ to answer part b.

Answer 2

For the second part, note that the portion (circumference) of ball is $\frac{2\pi/3}{2\pi}$ of the total circumference. Thus, arc $AB=2\pi r\times\frac{1}{3}=\frac{2}{3}\pi r$.

P.S.: The object here is a ball i.e., a sphere. Thus, length $AB$ doesn't makes any sense. $AB$ can have infinitely many values. Nevertheless, I considered it a circle, as you did for the first part. :)