# Finding equation for chord in terms of radius given angle theta

In this problem, I am trying to find the volume of the solid gotten by rotating the shaded area around the x-axis. The equation of a circle is $$x^2+y^2=r^2$$. If I am integrating using the shell method, I know the height and radius that I need (height = $$\sqrt{r^2-y^2}$$ and radius = y). My upper limit of integration is r. My lower limit of integration is c. I also see that when making a right triangle, c is opposite my hypotenuse which - so maybe I can use the sine function?

How should I figure out how to put c in terms of r?

• Yes, $\frac12=\sin{30^\circ}=\frac{c}{r}$ – saulspatz Dec 20 '19 at 16:13

Yes you are right, you should continue by using the trigonometric sine function. Which leads to $$c = r.Sin(\theta)$$