Difference between revisions of "Volume of a Sphere"

Revision as of 09:58, 27 August 2017

Let's say that we want to find the volume of a sphere of radius $r$ using volumes of revolution.

We know that the equation of a circle of radius $r$ centered at the origin is

x^{2}+y^{2}=r^{2}.

The upper half semicircle is given by: $y={\sqrt {r^{2}-x^{2}}}.$

(insert picture of semicircle)

Now, we want to rotate the upper half semicircle around the $x$ -axis. This will give us a sphere of radius $r.$

(insert pictures)

@@ Line 1: / Line 1: @@
 Let's say that we want to find the volume of a sphere of radius <math>r</math> using volumes of revolution.
+We know that the equation of a circle of radius <math>r</math> centered at the origin is
+::<math>x^2+y^2=r^2.</math>
+The upper half semicircle is given by: <math>y=\sqrt{r^2-x^2}.</math>
+(insert picture of semicircle)
+Now, we want to rotate the upper half semicircle around the <math>x</math>-axis. This will give us a sphere of radius <math>r.</math>
+(insert pictures)