Question

Help with the following problem please

Answer 1

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 =
`\pi R^2=\pi7^2=49\pi`
Area of large shaded circle =
`\pi x^2=\pi5^2=25\pi`
Area of 4 small shaded circles =
`4\pi r^2=4\pi1^2=4\pi`
Total area of shaded circles =
`25\pi+4\pi=29\pi`

Shaded area as a fraction of that of the outer circle

`=(29\pi)/(49\pi)=29/49`