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AnnyKZ [126]
3 years ago
14

Help with the following problem please

Mathematics
1 answer:
Effectus [21]3 years ago
3 0
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 
=\frac{29\pi}{49\pi}=29/49

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