Radius of 1 button = r = 3x
Fabric required to cover 1 button = Area of the circle
= [tex]\pi r^{2}[/tex]
= [tex]\pi (3x)^{2}[/tex]
= [tex]9\pi x^{2}[/tex]
Total number of buttons = x
Fabric required to cover 1 button = [tex]9\pi x^{2}[/tex]
Fabric required to cover x buttons = [tex]x(9\pi x^{2} )[/tex]
[tex]=9\pi x^{3}[/tex]
Hence, fabric required to cover x buttons [tex]=9\pi x^{3}[/tex] sq. units
