Question

If the central angle of a circle has measure 100° and makes a minor arc with length 25, what is the radius?

Answer 1

Answer:

14

Step-by-step explanation:

The central angle is 100/360 or 5/18 of the full circle. This means that the length of the minor arc it forms is also 5/18 of the full circumference. We can set up an equation to represent this. (Let circumference = C.) The equation will be 25 = 5/18 * C, and when we solve for C, we get C = 90. Now, let's find the radius!

The circumference formula of a circle is C = 2πr, where r is the radius and C is the circumference. We are solving for r. We know that C = 90, and we can use 3.14 for π. When we plug these values in, we get 90 = 2 * 3.14 * r. When we simplify the right side, we get 90 = 6.28 r, and when we solve for r, we get r≈14. Hope this helps!