Final answer:
To find the radius of a quarter circle, use the formula for the circumference of a circle and solve for 'r'. Given that the perimeter of the quarter circle is 17.85 cm, the radius is approximately 11.356 cm.
Step-by-step explanation:
To find the radius of a quarter circle when given its perimeter, we can use the formula for the circumference of a circle, which is equal to 2πr. Since we have a quarter circle, we only need to find one-fourth of the circumference. Let's denote the radius as 'r'.
Given that the perimeter of the quarter circle is 17.85 centimeters, we can set up the equation: 1/4(2πr) = 17.85. Solving for 'r', we have:
1/4(2 × 3.14159 × r) = 17.85
0.5 × 3.14159 × r = 17.85
1.5708 × r = 17.85
r = 17.85 / 1.5708
r ≈ 11.356
Therefore, the radius of the quarter circle is approximately 11.356 centimeters.