## Surface area of solids of revolution

Determine the surface area of

• #### Variant 1

a cylinder with height $$v$$ and base radius $$r$$.

• #### Variant 2

a cone with height $$v$$ and base radius $$r$$.

• #### Variant 3

a sphere with radius $$r$$.

• #### Variant 4

a paraboloid resulting from the rotation of the curve $$y = c \sqrt x$$ for $$x \in [0, b]$$.

• #### Variant 5

a torus with radii $$r$$ a $$R$$, $$R > r$$.