Question 565452
A figure (or solid) similar to another is a scaled-up or scaled-down (or maybe even identical) version of the other one. All dimensions (length, width, radius, height, etc) are changed by the same factor. The area is changed by that factor squared, and the volume is changed by that factor cubed.
That's written in the equalities you show.
So if the ratio (scale factor) for height and radius of those cylinders is the fraction/ratio {{{a/b}}}
{{{r[1]/r[2]=h[1]/h[2]=a/b}}},
the surface areas are in the ratio {{{Area[1]/Area[2]=(a/b)^2=a^2/b^2}}}
You know that
{{{Area[1]/Area[2]=(a/b)^2=a^2/b^2=8*pi/(18*pi)=4/9}}}
{{{(a/b)^2=a^2/b^2=4/9}}} --> {{{a/b=sqrt(4/9)=sqrt(4)/sqrt(9)=2/3}}} -->{{{a^3/b^3=(a/b)^3=2^3/3^3=8/27}}}
So the surface area of the samaller cylinder is 4/9 of the surface area of the larger cylinder. The radius and height are 2/3 of those for the larger cylinder, and the volume is 8/27 of the volume of the larger cylinder.