Respuesta :
Answer:
Circumference of a circle A = [tex]389.7 \,\,inches[/tex]
Area of a circle A = 12081.1 square inches
Step-by-step explanation:
Let [tex]r[/tex] denotes radius of circle B.
Circle A has a radius that is five more than twice as long as the radius of circle B.
So,
Radius of circle A = [tex]5+2r[/tex]
Diameter of circle = 2 (radius of circle)
So,
Diameter of circle B = 2r
Diameter of circle A = [tex]2(5+2r)[/tex]
Sum of the diameters of the circles A and B = [tex]2r+2(5+2r)[/tex]
[tex]=2r+10+4r[/tex]
[tex]=6r+10[/tex]
As sum of the diameters of the circles is 88 inches,
[tex]6r+10=88\\6r=78[/tex]
[tex]r=13[/tex] inches
Radius of a circle A = [tex]2(5+2r)[/tex]
[tex]=2[5+2(13)][/tex]
[tex]=2(5+26)[/tex]
[tex]=2(31)[/tex]
[tex]=62[/tex] inches
Let R denotes radius of a circle A.
R = 62 inches
Circumference of a circle [tex]=2\pi R=2\pi (62)=124\pi =124(\frac{22}{7})=389.7 \,\,inches[/tex]
Area of a circle [tex]=\pi r^2=\pi (62)^2=3844\pi=3844(\frac{22}{7})=12081.1[/tex] square inches
