Answer:
see explanation
Step-by-step explanation:
the arc length of a circle is calculated as
arc = circumference of circle × fraction of circle
(5)
circumference (C) is calculated as
C = 2πr ( r is the radius )
here diameter = 12 , then r = 12 ÷ 2 = 6
C = 2π × 6 = 12π ≈ 37.7 m ( to the nearest tenth )
(6)
JK = 2πr × [tex]\frac{75}{360}[/tex]
= 2π × 7 × [tex]\frac{5}{24}[/tex]
= 14π × [tex]\frac{5}{24}[/tex]
= [tex]\frac{14\pi (5)}{24}[/tex] ≈ 9.2 in ( to the nearest tenth )
(7)
7.5 = 2πr × [tex]\frac{120}{360}[/tex]
7.5 = 2πr × [tex]\frac{1}{3}[/tex] ( multiply both sides by 3 to clear the fraction )
22.5 = 2πr ( divide both sides by 2π )
r = [tex]\frac{22.5}{2\pi }[/tex] ≈ 3.6 ft