contestada

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?

Respuesta :

SaniShahbaz

Answer:

The diameter of the circle is 10 cm.

Step-by-step 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:

[tex]s\:=\:r\theta[/tex]

where

  • [tex]r[/tex] is the radius of the circle
  • [tex]\theta[/tex] is the central angle in radians

First lets find r,

[tex]\:\frac{s}{\theta \:}\:=\:r[/tex]

[tex]\frac{6}{1.2\:}\:=\:r[/tex]         ∵ s = 6 cm and [tex]\theta[/tex] = 1.2 radians

[tex]\:r\:=\:5\:cm[/tex]

As

  • Diameter 'd' is 2r.

so

[tex]d\:=\:2r[/tex]

[tex]d\:=\:2\left(5\right)[/tex]

[tex]d = 10[/tex] cm

Therefore, the diameter of the circle is 10 cm.

Answer:

Its 10 cm

Step-by-step explanation: