Question

. How are the formulas for the circumference of a circle and area of a circle derived?

Answer 1

They can be derived by using calculus(integration to be precise)

$\pi$$= \frac{circumference }{diameter}$(its how pi is defined)
so that gives circumference

to get area , you use integration $of an elemental ring of radius r and thickness dr and integrate it$$A= \int\limits^0_r {2 \pi r} \, dr$

that gives the area.

if you don't know calculus yet ,dont worry, just remember the formulae.