Finding components of a circle.

Question

I'm working on some summer problems so that I can be more prepared when I go into my class in the fall. I found a website full of problems of the content we will be learning but it doesn't have the answers. I need a little guidance on how to do this problem.

The following diagram shows a circle with centre o and radius 5 cm.
The points A, B, and C like on the circumference of the circle, and $\angle AOC$ = 0.7 radians.
a. Find the length of the arc ABC.
b. Find the perimeter of the shaded sector.
c. Find the area of the shaded sector.

For a, the arc length would be the angle multiplied by the radius, correct?

l = 5 x 0.7
l = 3.5 cm

For b, would it be 2 radii and the length of the arc added together?
5+5+3.5 = 13.5 cm

And for c, I’m honestly not too sure. Is it the central angle over 360° = the sector over $πr^2$

Answer 1

For point $a$ and $b$ your answers are correct.

For the area we have that for the whole circle

• $A(2\pi)=\pi r^2=\frac12 \cdot 2\pi\cdot r^2$

therefore for an angle $\theta$ since the area is proportional to the angle

• $A(\theta)=\frac12 \theta r^2$

with $\theta$ expressed in radians.