Area and Perimeter of Dilated Figures

Your pupils dilate naturally in response to different amounts of light. In the dark, the normal pupil size in adults can be $\text{4-8mm}$ in diameter, while $\text{2-4mm}$ in bright light. According to the BrightFocus Foundation, doctors use eye drops to dilate your pupils, letting in more light so they can see more of your retina. $\\$

Assume at normal pupil size, a doctor can only see about $1\text{mm}^{2}$ of your retina. How much more can they see if they use dilating eye drops. $\\$ Assume the affect of darkness and dilating eye drops are the same. $\\$ Assume the minimum sizes and maximum sizes correspond ($\text{2mm}$ dilates into $\text{4mm}$, $\text{3mm}$ dilates into $\text{6mm}$, $\text{4mm}$ dilates into $\text{8mm}$ and so on).