Question

A central angle of a circle measures 1.2 radians, and the length of the related intercepted arc measures 6 cm. What is the diameter of the circle?

Answer 1

Its 10 cm

Explanation:

Answer 2

The diameter of the circle is 10 cm.

Explanation:

As

• A central angle of a circle measures 1.2 radians, and

• The length of the related intercepted arc measures 6 cm.

The arc length formula is given by:

`s\:=\:r\theta`

where

• 
  `r` is the radius of the circle

• 
  `\theta` is the central angle in radians

First lets find r,

`\:(s)/(\theta \:)\:=\:r`

`(6)/(1.2\:)\:=\:r` ∵ s = 6 cm and
`\theta` = 1.2 radians

`\:r\:=\:5\:cm`

As

• Diameter 'd' is 2r.

so

`d\:=\:2r`

`d\:=\:2\left(5\right)`

`d = 10` cm

Therefore, the diameter of the circle is 10 cm.