# Arc length and surface area of parametric equations

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##### Intros

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##### Examples

###### Lessons

**The Length of a Curve**

Find the length of each of the given parametric equations:**The Surface Area of a Curve rotating about the x-axis**

Find the surface area for each of the given parametric equations by rotating about the $x$-axis:**Applications related to Circles and Spheres**

You are given the parametric equations $x=r\; \cos(t)$, $y=r\;\sin(t)$ where $0 \leq t \leq 2\pi$. Show that the circumference of a circle is $2\pi r$- You are given the parametric equations $x=r\; \cos(t)$, $y=r\;\sin(t)$ where $0 \leq t \leq \pi$. Show that the surface area of a sphere is $4\pi r^2$