Question

I know it's on edge but please explain the process instead of just giving the answers!!! Consider circle C with radius 5 cm and a central angle measure of 60°. Circle C is shown. Line segments RC and SC are radii with a length of 5 cm. Angle RCS is 60 degrees. What fraction of the whole circle is arc RS? What is the approximate circumference of the circle? What is the approximate length of arc RS?

Answer 1

Arc RS represents 1/6 of the entire circle. The approximate circumference of the circle is 31.4 cm, and the approximate length of arc RS is 5.24 cm.

Step-by-step explanation:

When considering circle C with radius 5 cm and a central angle measure of 60°, we can determine the fraction of the entire circle that arc RS represents by comparing the angle to the full 360° of a circle. A 60° angle is ⅖ of 360°, so arc RS represents ⅖ of the whole circle.

To find the approximate circumference of the circle, we use the formula C = 2πr, where 'C' is the circumference and 'r' is the radius. Substituting the given radius, 5 cm, we get C ≈ 2π(5 cm) ≈ 31.4 cm. Finally, to find the approximate length of arc RS, we take the fraction of the circle that arc RS represents and multiply it by the circumference, so the arc length (AS) is ⅖(31.4 cm) ≈ 5.24 cm.