Question

If the diameter of a circle is 6 inches, how long is the arc subtended by an angle measuring 70°? A) 3 7 π inches B) 6 7 π inches C) 7 2 π inches D) 7 6 π inches

Answer 1

Option D

The length of arc is $\frac{7}{6} \pi$ inches

Solution:

Given that diameter of a circle is 6 inches

To find: length of arc subtended by an angle measuring $70^\circ$

The length of arc when angle is measured in degrees is given as:

$\text {arc length }=\frac{\theta}{360} \times 2 \pi r$

Where,

$\theta$ is the central angle in degrees

"r" is the radius of circle

Given that diameter  = 6 inches

$Radius = \frac{diameter}{2}$

$radius = \frac{6}{2} = 3 inches$

Substitiute r = 3 inches and $\theta = 70 degrees$ in arc length formula

$\begin{array}{l}{\text { arc length }=\frac{70}{360} \times 2 \pi(3)} \\\\ {\text { arc length }=\frac{7}{36} \times 6 \pi=\frac{7}{6} \pi}\end{array}$

Thus length of arc is $\frac{7}{6} \pi$ inches So option D is correct