In a circle, a 225 degrees sector has area 490pi in2. What is the radius of the circle?
Accepted Solution
A:
we know that
area of a sector=(∅*pi/360°)*r²--------> when ∅ is in degree r=√[360°*(area of a sector)/(∅*pi)]
area of a sector=(∅/2)*r²--------> when ∅ is in radians r=√[2*(area of a sector)/∅]
let's calculate the radius of the two ways
1) r=√[360°*(area of a sector)/(∅*pi)] area of a sector=490*pi in² ∅=225° r=√[360°*(490*pi)/(225°*pi)]-------> r=√784-----> r=28 in
2) r=√[2*(area of a sector)/∅] area of a sector=490*pi in² ∅=225°-----> convert to radians-----> ∅=225°*pi/180-----> ∅=1.25*pi r=√[2*(490*pi)/(1.25*pi)]----> r=√[980/1.25]---> r=√784----> r=28 in