Volume, surface area and similarity
Volume is base area times height, a third of that for a cone; similar shapes scale every length equally.
A worked example
A cylinder of radius 5 cm and height 6 cm has volume 3.14 x 5² x 6 = 471 cm³.
The mistake people actually make
Use the radius in πr², not the diameter. Surface area covers every face, so a cube needs six squares counted, not one.