Mathematico | Mathematico

A cylinder has a radius $r$ and a height given by

h = r + 2 + \frac{1}{r}

Cylinder of radius r and height r + 2 + 1/r

A fully factorised expression for the volume of the cylinder, in terms of $r$ , can be given in the form

π r (r + a)^{b}

where $k \in R$ and $a, b, c \in Z$ .

Give

π (a + b)

to three significant figures

Hint

The volume, $V,$ of a cylinder is given by $V = π r^{2} h .$

Solution

The volume, $V,$ of a cylinder is given by

\begin{aligned} V & = π r^{2} h \\ = π r^{2} (r + 2 + \frac{1}{r}) \\ = π r (r^{2} + 2 r + 1) \\ = π r (r + 1)^{2} \end{aligned}