Question

The center of the circle below is at P. If the central angle < APB measures 101 °, and the length of arc AB = 22 cm., find the radius. (round to the nearest tenth)

Answer 1

Explanation:

we need to remember :

a full circle is 360°.

and the circumference is

2×pi×r

so, due to the given degrees we know that AB corresponds to 101/360 of a whole circle. this ratio applies to the degrees as well as to the arc lengths in relation to the circumference.

therefore,

22 cm = 101/360 × 2×pi×r = 101/180 × pi×r

3960 = 101 × pi×r

r = 3960 / (101×pi) = 12.4802688... ≈ 12.5 cm

Answer 2

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

circle diagram

Step 02:

arc length of a circle:

angle APB = 101°

arc AB = 22 cm

radius:

`arc\text{ length = }(\theta)/(360\degree)*2\pi r`
`\begin{gathered} 22\text{ cm = }(101\degree)/(360\degree)*2\pi r \\ \\ 22\text{ cm * }(360\degree)/(101\degree)\text{ * }(1)/(2\pi)\text{= r} \\ \\ 12.480\text{ cm = r} \end{gathered}`

The answer is:

radius = 12.5 cm