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.

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
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