Surds - Applications of Surds

A cylinder has a radius of \(\left( \sqrt{2}-1 \right)\mathrm{ cm}\) and a volume of \(\left( 12+4\sqrt{2} \right)\pi \mathrm{ c}{{\mathrm{m}}^{\mathrm{3}}}\). Find, without using a calculator, the exact value of its height, \(h\) , in the form \(\frac{a+b\sqrt{2}}{c}\)cm, where \(a\), \(b\) and \(c\) are integers.