Almost all telescopes have a circular mirror. The area of a circle is proportional to [tex]r^2[/tex] where [tex]r[/tex] is the radius of the circle, the constant of proportionality being [tex]4\pi[/tex]
[tex]S =4\pi r^2[/tex]
Therefore the area of 150 meter telescope would be
[tex]S_1/S_2=(r_1/r_2)^2 =(75/5)^2 =15^2=225[/tex]
times bigger than the area of the smaller (10 meter) telescope.
