Question

Question #59ecb

Answer 1

See below

Explanation:

Let be `s = L/n` where `L` is the circumference length and `n` the number of slices used.

For each slice we have `b approx s` where `b` is the slice (triangle with vertice at the circle's center) basis

Each triangle has an area giving by

`a =( bxx h)/2` where `h = sqrt(r^2-(b/2)^2)` (Pythagoras).

but `b approx s = L/n` so

`A = lim_(n->oo)n(1/2)(L/n) sqrt(r^2-(L/(2n))^2) = L r/2`

but `L = 2 pi r` so finally

`A = pi r^2`