Question #59ecb

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Answer 1 · 2016-09-10T17:19:17

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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#