Question

What is the length of an arc cut off by an angle of 2.75 radians on a circle of radius 5 inches?

Answer 1

Explanation:

The angle subtended by an arc is the ratio of arc length to radius of the circle the arc is a part of. Writing it down mathematically,

`\boxed{ \large{ \theta = (s)/(r) }}`

where
`\theta` is expressed in radians and s,r in m. 5 inches = 0.127 m (approx.)

In the question, the values of
`\theta` and R is given, we can substitute to find the value of s:

`\hookrightarrow 2.75 = \large{(s)/(0.127 \: m) }`

`\hookrightarrow s = 2.75 * 0.127 \: m`

`\hookrightarrow \: s = 0.34925 \: m`

`\therefore` Length of the arc is 0.34925 m or 34.925 cm.