Circle b:
Diameter = x
Radius = [tex] \frac{x}{2} [/tex]
Area = [tex] \pi r^{2} = \pi ( \frac{x}{2} )^{2} = \frac{ \pi x^{2} }{4} [/tex]
Circle a:
Diameter = [tex] \frac{x}{2} [/tex]
Radius = [tex] \frac{x}{2} * \frac{1}{2} = \frac{x}{4} [/tex]
Area = [tex] \pi r^{2} = \pi ( \frac{x}{4} )^{2} = \frac{ \pi x^{2} }{16} [/tex]
Thus,
Area of circle b to area of circle a
= [tex]\frac{ \pi x^{2} }{4} [/tex] ÷ [tex]\frac{ \pi x^{2} }{16} [/tex]
= [tex]\frac{ \pi x^{2} }{4} [/tex] × [tex]\frac{ 16 }{\pi x^{2}} [/tex]
= 4
Hence, the area of circle b is 4 times the area of circle a.
