Question

the diameter is 24 cm. find the length of arc cd.
arc: ____________

Explanation:

Step1: Find the radius of the circle

The diameter \( d = 24 \) cm, and the radius \( r=\frac{d}{2}=\frac{24}{2} = 12 \) cm.

Step2: Recall the formula for arc length

The formula for the length of an arc with central angle \( \theta \) (in degrees) is \( L=\frac{\theta}{360^\circ}\times2\pi r \). Here, \( \theta = 60^\circ \) and \( r = 12 \) cm.

Step3: Substitute the values into the formula

\( L=\frac{60^\circ}{360^\circ}\times2\pi\times12 \)
First, simplify \( \frac{60^\circ}{360^\circ}=\frac{1}{6} \). Then, \( 2\pi\times12 = 24\pi \). So, \( L=\frac{1}{6}\times24\pi = 4\pi \) cm. If we take \( \pi\approx3.14 \), then \( L\approx4\times3.14 = 12.56 \) cm.

Answer:

The length of arc \( CD \) is \( 4\pi \) cm (or approximately \( 12.56 \) cm).