Answer:
a) A₁ /A₂ = r₁² / (r₂² - r₁²)
b) A₂ /A₃ = (r₂² - r₁²) / (r₃² - r₂²)
Step-by-step explanation:
We have Circle 1 and area A₁
Area of circle 2 outside circle 1 = A₂
Area of circle 3 outside circle 2 = A₃
On the other hand we have
A₁ = π*r₁² area of circle 1
A₂´ = π*r₂² area of circle 2
A₃´ = π*r₃² area of circle 3
All areas in cm²
a) A₁ /A₂
A₁ = π*r₁²
According to problem statement A₂ = π*r₂² - A₁
A₂ = π*r₂² - π*r₁² ⇒ A₂ = π* (r₂² - r₁²)
Then A₁ /A₂ = π*r₁² / [π* (r₂² - r₁²)]
A₁ /A₂ = r₁² / (r₂² - r₁²)
b) A₂ /A₃
A₂ = π* (r₂² - r₁²)
And
A₃ = π* (r₃² - r₂²)
Therefore
A₂ /A₃ = π* (r₂² - r₁²) / π* (r₃² - r₂²) ⇒ A₂ /A₃ = (r₂² - r₁²) / (r₃² - r₂²)
A₂ /A₃ = (r₂² - r₁²) / (r₃² - r₂²)
