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

 The area of the complete circle is:
 [tex]A = pi * r ^ 2 [/tex]
 Where,
 r: radius of the circle.
 Substituting values we have:
 [tex]A = \pi * (10/2) ^ 2 A = \pi * (5) ^ 2 A = 25 \pi [/tex]
 Then, the measure of the angle of the arc whose area is 5pi is given by:
 [tex]theta = A '/ A * (360) [/tex]
 Where,
 A '/ A: ratio of areas
 Substituting values:
 [tex]theta = (5 \pi / 25 \pi ) * (360) theta = (5/25) * (360) theta = (1/5) * (360)  theta = 72 degrees[/tex]
 Answer:
 the angle measure of an arc bounding to sector area 5pi square meters is:
 theta = 72 degrees