i need help with this

Question

the area of a sector of a circle with angle 45 degress is 4 square feet. find the radius of the circle. if your computation involves pi, use pi=3.14159. round to 2 decimal places.

Answer 1

(45°/360°)(pi r^2) = 4

 

(pi/8)(r^2) = 4

 

r^2 = 32/pi

 

r = √(32/3.14159) ≈ 3.19153959110083 ≈ 3.19 feet

Answer 2

Using:

 

A = n × πr²

     360

 

where

A = 4

n = 45°

π = 3.14159

 

Input the given values;

 

4 = (45) × (3.14159)r²

       360

 

4 =    1    × (3.14159)r²

         8

 

4 = (3.14159)r²

            8

 

Cross multiply

 

(4)(8) = (3.14159)r²

 

32 = (3.14159)r²

 

To solve for r, divide both sides by (3.14159)

 

      32      = (3.14159)r²

 (3.14159)     (3.14159)

 

      32      = r²

(3.14159)

 

Rewrite the equation

 

r² =    32    

       (3.14159)

 

r² = 10.186

 

r = √(10.186)

 

r = 3.192

 

Rounded to 2 decimal places we'd have;

 

r = 3.20

Answer 3

360/45=8 sectors, each 4 square feet

the area of the circle is 8*4=32 square feet

A=pi* r^2

32=3.14159*r^2

32/(3.14159)=r^2

10.18592496=r^2

√(10.18592496)=r

3.191539591=r

r=3.19 feet