Step: 1

The given arc length is 6 cm and the central angle is 40 degrees.

To find the radius of the circle, we can use the formula relating the arc length, central angle, and radius: \$"arc length" = "radius" \times "central angle"\$

Substituting these values into the formula, we have: \$6 cm = r \times 40 "degrees"\$

The angle to be in radians rather than degrees. Since 1 radian is equal to \$(180 "degrees") / π\$, we can convert the angle to radians.

\$40 "degrees" = (40 "degrees") \times (π / 180 "degrees") \$

=\$(2π / 9) "radians"\$

Now we can rewrite the equation as: \$6 cm = r \times (2π / 9)\$ radians

\$6 / (2π / 9) = r\$

\$r = (54 cm) / π\$ radians

Thus, the radius of the circle is 17.1828 cm.

Explanation: