# Polar Regions: Area, Arc Length, and Surface Area

## Homework Statement

Consider the graph (see attachment) of r = 1 +2cos$$\Theta$$ in polar coordinates. SET UP integrals to find
1. the area inside the large loop minus the area of the small loop.
2. the arc length of the small loop
3. the surface area of the surface formed by revolving the large loop about the initial ray.

## Homework Equations

area A of the polar region
A = $$\int$$$$\frac{1}{2}$$(f($$\Theta$$))$$^{2}$$d$$\Theta$$ with upper limit b and lower limit a.

arc length AL of the polar region:
AL = $$\int$$$$\sqrt{r^{2}+(\frac{dr}{d\Theta})^{2}} d\Theta$$ with upper limit b and lower limit a.

not sure what equation i need to figure out the surface area one

## The Attempt at a Solution

I'm pretty much lost when it comes to the entire problem, and have no ideas where to start. Please help!

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