The diameter of a circle is 10m. What is the angle measure of an arc bounding a sector area 5pi square meters?

Answer:
Angle measure of an arc is 72 °.
Step-by-step explanation:
Given : The diameter of a circle is 10m and sector area 5pi square meters.
To find : What is the angle measure of an arc .
Solution : We have given that Diameter = 10 cm .
Radius = [tex]\frac{10}{2}[/tex] = 5 cm.
Area of sector = [tex]\frac{theta}{360} *pi (r^{2} )[/tex].
Plugging the values of r = 5cm , Area of sector = 5 pi.
5 pi = [tex]\frac{theta}{360} *pi (5^{2} )[/tex].
5 pi = [tex]\frac{theta}{360} *pi (25 )[/tex].
On dividing by 25 pi
[tex]\frac{5\ pi}{25\ pi}[/tex] = [tex]\frac{theta}{360})[/tex].
[tex]\frac{1}{5}[/tex] = [tex]\frac{theta}{360})[/tex].
On multiplying both sides by 360 and swtiching sides.
Theta = [tex]\frac{360}{5}[/tex].
Theta = 72 °
Therefore, angle measure of an arc is 72 °.