Answer:
r ≈,22.9 units
Step-by-step explanation:
The central angle EQF is equal to the arc FE that subtends it.
central angle EFQ = 100°
The length of an arc of a circle is calculated as
length = circumference of circle × fraction of circle
= 2πr × [tex]\frac{EFQ}{360}[/tex] ( r is the radius )
given arc length is 40 units , then
2πr × [tex]\frac{100}{360}[/tex] = 40
2πr × [tex]\frac{10}{36}[/tex] = 40 ( multiply both sides by 36 to clear the fraction )
2πr × 10 = 36 × 40 = 1440
20πr = 1440 ( divide both sides by 20π )
r = [tex]\frac{1440}{20\pi }[/tex] ≈ 22.9 units ( to the nearest tenth )
