The area of a circle of radius r is πr^2, which happens to be 1/2r times the circumference

2Ï€r. Explain why this relationship should be expected.

5 answers

the weird ie thing is supposed to be pi
Area = π r^2
circumference = 2πr

Area/circumference = πr^2 /(2πr) = r/2
2(Area) = r(circumference)
Area = (r/2)(circumference)
as required to show
why would it be expected though?
Well, were you surprised when the result popped out, was it un-expected ??
no, ok thanks
i have one more question...

Consider a billion-sided regular polygon that is circumscribed around a circle of radius r; how are its area and perimeter related?