Question

the length of an arc of a circle with diameter 24cm is 20πCM the central angle of this arc is
(a) 120°
(b) 300°
(c) 75°
(d) 150°​

Answer 1

The central angle of this arc is 300 degrees

Answer 2

Given,

The diameter of the circle

$d=24cm$

$r=\frac{d}{2}$

$r=\frac{24}{2}$

$r=12cm$

Length of the arc is $20\pi cm$

Now, we know that

Length of arc$=2 \pi r\times \theta /360$

$20 \pi =2\times \pi \times 12\times \frac{\theta}{360}$

$20=\frac{\theta}{15}$

$\theta=15\times 20$

$\theta=300$

Therefore, the central angle of arc is $300$