Respuesta :
Option D
The length of arc is [tex]\frac{7}{6} \pi[/tex] inches
Solution:
Given that diameter of a circle is 6 inches
To find: length of arc subtended by an angle measuring [tex]70^\circ[/tex]
The length of arc when angle is measured in degrees is given as:
[tex]\text {arc length }=\frac{\theta}{360} \times 2 \pi r[/tex]
Where,
[tex]\theta[/tex] is the central angle in degrees
"r" is the radius of circle
Given that diameter = 6 inches
[tex]Radius = \frac{diameter}{2}[/tex]
[tex]radius = \frac{6}{2} = 3 inches[/tex]
Substitiute r = 3 inches and [tex]\theta = 70 degrees[/tex] in arc length formula
[tex]\begin{array}{l}{\text { arc length }=\frac{70}{360} \times 2 \pi(3)} \\\\ {\text { arc length }=\frac{7}{36} \times 6 \pi=\frac{7}{6} \pi}\end{array}[/tex]
Thus length of arc is [tex]\frac{7}{6} \pi[/tex] inches So option D is correct
