Solution:

r₁ = 21/2 cm is the radius of the first circle (as diameter D is given as 21 cm)

As a result, the area of the gold region = π r₁² = π(10.5)² = 346.5 cm².

Given that each of the remaining bands is 10.5 cm wide,

As a result, the radius of the second circle, r₂ = 10.5cm+10.5cm = 21 cm 

As a result, the area of the red zone = the area of the second circle − and the area of the gold region = (πr₂²−346.5) cm²

= (π(21)² − 346.5) cm²

= 1386 − 346.5

= 1039.5 cm²

In the same way,

r₃ = 21 cm+10.5 cm = 31.5 cm is the radius of 3^rd circle

r₄ = 31.5 cm+10.5 cm = 42 cm is the radius of 4^th circle

r₅ = 42 cm+10.5 cm = 52.5 cm is the Radius of 5^th circle

For the n^th regions ,area

A = Area of circle n – Area of circle (n-1)

Therefore, Area of blue region (n=3) = Area of third circle – Area of second circle

= π(31.5)² – 1386 cm²

= 3118.5 – 1386 cm²

= 1732.5 cm²

Therefore, Area of black region (n=4) = Area of fourth circle – Area of third circle

= π(42)² – 1386 cm²

= 5544 – 3118.5 cm²

= 2425.5 cm²

Therefore, Area of white region (n=5) = Area of fifth circle – Area of fourth circle

= π(52.5)² – 5544 cm²

= 8662.5 – 5544 cm²

= 3118.5 cm²