Parametric Calculus: Surface Area: Example 1: Sphere

In this video I go over an example using the surface area formula for parametric curves, and this time use it to determine the surface area of a sphere with radius r. To do this I first visually show the parametric equations of a circle, and then form a sphere by rotating the top semi-circle about the x-axis. From here I show how we can write the symbolic representation to better memorize the surface area formula, and then after applying the formula, we can then integrate to get the surface area of a sphere, which is 4*pi*r^2. This is a very important video because it shows how we can use parametric curves and equations to determine the relatively famous equation for the surface of a sphere, which adds to the number of ways we can determine a formula. This is a good example in showing that the theorems we create are correct by using them to calculate famous equations, so make sure to watch this video!

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I don't always determine the surface area of a sphere but when I do I usually use the parametric equations of a circle to do so ;)


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