Question

A circle has a diameter of 24 centimeters. Central angle FOG is drawn, determining an arc FG. The radian measure of angle FOG is 3/4 What is the length of arc FG in centimeters?16 cm9 cm32 cm18 cm

Answer 1

9 cm

Step-by-step explanation:

We are given the following information:

Diameter = 24 cm

Angle FOG = 3/4 rad

The formula for calculating arc length is written below:

`\begin{gathered} L=\theta* r \\ where\colon \\ \theta=central\text{ angle of }arc,\text{ in }rad \\ r=radius \\ r=\frac{\text{Diameter}}{2}=(24)/(2)=12cm \\ \theta=(3)/(4)rad \\ \text{Substitute these into the formula, we have:} \\ L=(3)/(4)*12 \\ L=(3*12)/(4) \\ L=9cm \\ \\ \therefore L=9cm \end{gathered}`

Therefore, the arc length is 9 cm