Question

If two concentric circles have radii of 4 cm and 5 cm, how much longer, in cm, is the intercepted arc in the larger circle than an intercepted arc in the smaller circle for a central angle that is π2 radians?

Answer 1

`(\pi)/(2) cm`

Explanation:

Given two concentric circles where:

• Radius of the Larger Circle =5
• Radius of the smaller circle=4

Length of the intercepted arc for a central angle of
`(\pi)/(2) =((\pi)/(2) )/(2\pi) X2\pi r=(\pi r)/(2)`

For the larger circle of radius 5cm, Length of the intercepted arc
`=(5\pi)/(2)`

For the smaller circle of radius 4cm, Length of the intercepted arc
`=(4\pi)/(2)`

Difference in Arc length

`=(5\pi)/(2)-(4\pi)/(2)\\=(\pi)/(2) cm`