Answered

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A circle has a diameter of 16 centimeters. Central angle FOG is drawn, determining an arc FG. The radian measure of angleFOG is 2. What is the length of arc FG in centimeters?12 cmO4 cm0 3232 cmO 6 cm

A Circle Has A Diameter Of 16 Centimeters Central Angle FOG Is Drawn Determining An Arc FG The Radian Measure Of AngleFOG Is 2 What Is The Length Of Arc FG In C class=

Sagot :

ANSWER

6cm

EXPLANATION

Given;

[tex]\begin{gathered} d=16cm \\ r=\frac{d}{2}=\frac{16}{2} \\ =8 \\ \theta=\frac{3}{4}\times\frac{180}{\pi} \\ =42.972 \end{gathered}[/tex]

Hence, recall the formula for calculating length of arc is;

[tex]\frac{\theta}{360}\times2\pi r[/tex]

Substitute the values;

[tex]\begin{gathered} \frac{\theta}{360}\times2\pi r \\ \frac{42.9718}{360}\times2\times3.142\times8 \\ =\frac{2160.18}{360} \\ =6 \end{gathered}[/tex]

Therefore, the length of the arc FG is 6cm

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