Answer:
[tex]Diameter = 16[/tex]
Step-by-step explanation:
Given
[tex]\theta = 72[/tex]
[tex]Sector = \frac{64}{5}\pi[/tex]
Required
Calculate the diameter
The area of a sector is:
[tex]Area = \frac{\theta}{360} * \pi r^2[/tex]
Substitute values for Area and [tex]\theta[/tex]
[tex]\frac{64}{5}\pi = \frac{72}{360} * \pi r^2[/tex]
Divide both sides by [tex]\pi[/tex]
[tex]\frac{64}{5} = \frac{72}{360} * r^2[/tex]
Make [tex]r^2[/tex] the subject
[tex]\frac{64*360}{5*72} = r^2[/tex]
[tex]\frac{64*360}{360} = r^2[/tex]
[tex]64 = r^2[/tex]
Take positive square roots of both sides
[tex]\sqrt{64} = r[/tex]
[tex]8 = r[/tex]
[tex]r = 8[/tex]
The diameter is then calculated as:
[tex]Diameter = 2r[/tex]
[tex]Diameter = 2*8[/tex]
[tex]Diameter = 16[/tex]
