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

Given

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 then simplify:

\$r = (20cm) / (\cancel(120)^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 is an incorrect answer; it’s slightly larger than the valid value

Wrong 9.59 cm

9

Choice-B

This is correct because it matches the calculated radius based on the given arc length and central angle

Correct 9.55 cm

10

Choice-C

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

Wrong 9.57 cm

11

Choice-D

This is an incorrect answer; it seems to be an inaccurate value by using the formula

Wrong 9.058 cm

12

Answer

Option

B

13

Sumup

Please summarize choices