MATH SOLVE

4 months ago

Q:
# 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

the answer is

the radius is 28 in

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

the answer is

the radius is 28 in