Question

What is the length of radius to the nearest tenth of an inch?

Answer 1

3.1 in

Explanation:

In any circle the following ratios are equal

`(arc)/(circumference)` =
`(angleatcentre)/(2\pi )`

`(4)/(2r\pi )` =
`((5\pi )/(12) )/(2\pi )`

`(4)/(2r\pi )` =
`(5)/(24)` ( cross- multiply )

10πr = 96 ( divide both sides by 10π )

r =
`(96)/(10\pi )` = 3.1 in ( nearest tenth )

Answer 2

radius = arc length / central angle in radians

radius = 4 inches / 5*PI / 12

radius = 4 / 1.308996939 radians

radius = 3.0557749074

radius = 3.0557749074 inches

Explanation: