Question

what is the length of an arc subtended by an angle of 1.25 radians in a circle with a diameter of 24 cm?​

Answer 1

15 cm.

Explanation:

Recall that the arc-length of a circle is given by the formula:

`\displaystyle s = r\theta`

Where r is the radius and θ is the measure of the central angle in radians.

The circle has a diameter of 24 cm, so its radius is 12 cm.

And its central angle is 1.25 radians. Hence, the arc-length will be:

`\displaystyle s = \left(12\right)\left(1.25\right) = 15\text{ cm}`

In conclusion, the arc-length for a circle with a diameter of 24 cm subtended by a central angle of 1.25 radians is 15 cm.