A sector of area 17 square feet is formed by a central angle of 154.6986 ∘ 154.6986∘. Find the radius of the circle?

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Answer 1 · 2018-02-24T22:40:59

#color(blue)(r=3.5486ft)#

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In Circle #O#, radii #OA# and #OC# enclose the sector #OABC# which has a central angle of:

#color(red)(/_AOC=154.6986^@)#

The area of the sector is:

#color(red)(A_("sector")=17sqft)#

Area of the circle is:

#A_("circle") = (A_("sector")/154.6986^@)(360^@)=17/154.6986*360#

#color(purple)(A_("circle")=39.5608sqft)#

The formula for area of a circle is #pir^2# where #r# is the radius.

#pir^2=39.5608#

#r^2=39.5608/pi=12.5926#

#color(blue)(r=3.5486ft)#