Given:
The largest circle has a radius of R=7 units.
Let x be the radius of the large shaded circle.
The small shaded circles have a radius of 1/5 of the large shaded circle.
=> the small shaded circles have a radius of r=x/5
By adding up radii, we have the equation
2(r+x+r)=2(x/5+x+x/5)=2R=2*7=14
Simplify:
7x/5=14/2
x=5
=> r=1
Area of outer circle = [tex]\pi R^2=\pi7^2=49\pi[/tex]
Area of large shaded circle = [tex]\pi x^2=\pi5^2=25\pi[/tex]
Area of 4 small shaded circles = [tex]4\pi r^2=4\pi1^2=4\pi[/tex]
Total area of shaded circles =[tex]25\pi+4\pi=29\pi[/tex]
Shaded area as a fraction of that of the outer circle
[tex]=\frac{29\pi}{49\pi}=29/49[/tex]
