Set up a Riemann sum approximating the volume of the torus (donut)obtained by rotating the circle $(x-6)^{2}+y^{2}=1$ about the y-axis.
A) $\sum \pi\left(6+\sqrt{1-y^{2}}\right)^{2} \Delta y$
B) $\sum \pi\left(6-\sqrt{1-y^{2}}\right)^{2} \Delta y$
C) $\sum \pi\left(\left(6+\sqrt{1-y^{2}}\right)^{2}+\left(6-\sqrt{1-y^{2}}\right)^{2}\right) \Delta y$
D) $\sum \pi\left(\left(6+\sqrt{1-y^{2}}\right)^{2}-\left(6-\sqrt{1-y^{2}}\right)^{2}\right) \Delta y$

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The Answer of Set up a Riemann sum approximating the volume of the torus (donut)obtained by rotating the circle $(x-6)^{2}+y^{2}=1$ about the y-axis.
A) $\sum \pi\left(6+\sqrt{1-y^{2}}\right)^{2} \Delta y$
B) $\sum \pi\left(6-\sqrt{1-y^{2}}\right)^{2} \Delta y$
C) $\sum \pi\left(\left(6+\sqrt{1-y^{2}}\right)^{2}+\left(6-\sqrt{1-y^{2}}\right)^{2}\right) \Delta y$
D) $\sum \pi\left(\left(6+\sqrt{1-y^{2}}\right)^{2}-\left(6-\sqrt{1-y^{2}}\right)^{2}\right) \Delta y$

Set Up a Riemann Sum Approximating the Volume of the Torus