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Problem 5 modelling

A cylinder has a radius r and a height given by

h=r+2+1r

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

πr(r+a)b

where kR and a,b,cZ.

Give

π(a+b)

to three significant figures

Hint

The volume, V, of a cylinder is given by V=πr2h.

Solution

The volume, V, of a cylinder is given by

V=πr2h=πr2(r+2+1r)=πr(r2+2r+1)=πr(r+1)2