1

Problem

An arc length in a circle is 20 cm, and the central angle corresponding to the arc is 120 degrees. Find the radius of the circle.

2

Step

The given data is

s = 20 cm and θ = 120°

3

Formula

The arc length and the central angle: \$r = (s/θ) \times (180°)/π\$.

4

Step

Plug the given values into the formula and slove for r:

\$r = (20)/(\cancel120°^2) \times (\cancel(180°^3)/π)\$

\$r = (20)/2 \times (3/π)\$

5

Step

Calculate the r value:

\$r = (\cancel 20^10)/(\cancel 2^1) \times (3/π)\$

\$r = (30)/π\$

\$r = 9.55 cm\$

6

Solution

Therefore, the radius of the circle is 9.55 cm.

7

Sumup

Please summarize steps

Choices

8

Choice-A

This answer is incorrect; it is slightly larger than the valid value

Wrong 9.59 cm

9

Choice-B

It accurately represents the radius based on the given arc length and central angle

Correct 9.55 cm

10

Choice-C

This answer is incorrect; it is slightly smaller than the valid value

Wrong 9.57 cm

11

Choice-D

This answer is incorrect and appears to reflect an inaccurate value

Wrong 9.058 cm

12

Answer

Option

B

13

Sumup

Please summarize choices