Question

The perimeter of a quarter circle is 17.85 miles. What is the quarter circle’s radius?

Answer 1

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     $2r+\frac{\pi }{2}$   . We can  form an equation to work out the radius so,

$2r+\frac{\pi }{2}$  =    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