A circle of radius $\displaystyle {r}={1}$, centered at $\displaystyle {\left({6},{6}\right)}$ is revolved about the line $\displaystyle {x}=-{3}$. Using appropriate methods, write the two possible integrals that may be used to find the volume of the resulting solid. Then evaluate one of the integrals to determine the volume. Hint: The second integral represents an area of a common geometric figure.

Method 1

 $\displaystyle {V}={\int_{{5}}^{{7}}}$ $\displaystyle {\left.{d}{x}\right.}$     Preview Question 6 Part 1 of 3  

Method 2

 $\displaystyle {V}={\int_{{5}}^{{7}}}$ $\displaystyle {\left.{d}{y}\right.}$     Preview Question 6 Part 2 of 3  

The volume of the solid is $\displaystyle {V}=$  . Write your answer in terms of $\displaystyle \pi.$