Question

Determine the angle (in radians) subtended at the center of a circle of radius $3cm$ by arc of length of $6cm$ and $3\pi cm$ respectively.

• A. $2\pi$ and $\pi$
• B. $2$ and $\pi$
• C. $\pi$ and $2\pi$
• D. $3$ and $2$

Answer 1

The correct option is B $2$ and $\pi$

Let,
$S=$ arc length
$R=$ radius
$\theta =$ angle

We know,
$S=R\theta \to \theta =\frac{S}{R}$

For, $S=6cm$
$\theta =\frac{6}{3}=2rad$

For, $S=3\pi cm$
$\theta =\frac{S}{R}=\frac{3\pi }{3}=\pi rad$