Answer:
8.1
Step-by-step explanation:
The perimeter of a circle means the circumference. In this question it says the perimeter of a quarter circle is 17.85 miles and we want to find the quarter circle’s radius.
We know that the perimeter of the quarter circle is 17.85 which means that the 2 radii and the circumference of the circle sum to 17.85.
The formula to work out the perimeter of a quarter circle is [tex]2r+\frac{\pi }{2}[/tex] . We can form an equation to work out the radius so,
[tex]2r+\frac{\pi }{2}[/tex] = 17.85
→ Multiply everything by 2 to get rid of the fraction
4r + π = 35.7
→ Minus π from both sides to isolate 4r
4r = 32.55840735
→ Divide both sides by 4 to isolate 4
r = 8.139601837
The radius of the quarter circle is 8.1 miles to 1 decimal place
