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
`(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 }=(\theta)/(360) * 2 \pi r`

Where,

`\theta` is the central angle in degrees

"r" is the radius of circle

Given that diameter = 6 inches

`Radius = (diameter)/(2)`

`radius = (6)/(2) = 3 inches`

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

`\begin{array}{l}{\text { arc length }=(70)/(360) * 2 \pi(3)} \\\\ {\text { arc length }=(7)/(36) * 6 \pi=(7)/(6) \pi}\end{array}`

Thus length of arc is
`(7)/(6) \pi` inches So option D is correct