Respuesta :
Answer: 45°
Step-by-step explanation:
Diameter= 16m
Radius= 16/2 = 8m
The area of the circle= πr^2
= π8^2
= 64π square metres.
An area of 8π square metres is also 1/8 of the total area, therefore the arc must be 1/8 of the circumference.
The circumference = 2πr = 16π,
This gives us an arc length of 2π metres.
But since we are looking for the the angle.
In degrees: 360/8 = 45°
The angle of the sector is 45 degrees.
To understand the calculations, check below
Sector of circle:
The radius of circle is [tex]\frac{16}{2} =8cm[/tex]
The area of circle is,
[tex]Area=\pi*8^{2} \\\\Area=64 \pi[/tex]
Area of sector [tex]=8\pi[/tex]
Angle of sector,
[tex]=\frac{8\pi}{64\pi} *360\\\\=\frac{360}{8}=45 degrees[/tex]
The angle of sector is 45 degrees.
Learn more about the sector angle here:
https://brainly.com/question/22972014
