Volumes of solids of revolution
Task number: 3145
Determine the volume of
Variant 1
a cylinder with height \(v\) and a base radius \(r\).
Variant 2
a cone with height \(v\) and base radius \(r\).
Variant 3
a sphere with radius \(r\).
Variant 4
a torus with radii \(R\) and \(r\), \(R > r\).
Variant 5
an infinite „funnel“ resulting form the rotation of \(f(x) = \frac{1}x\) for \(x \in [1,\infty]\) around the \(x\) axis.
Variant 6
a solid of revolution resulting from the rotation of the function \(y = \root 3 \of x\) for \(y \in[1, 2]\) around the \(y\) axis.