Exersice 12.1 ka 3 no

The radius of 1^st circle, r₁ = 21/2 cm (as diameter D is given as 21 cm)

So, area of gold region = π r₁² = π(10.5)² = 346.5 cm²

Now, it is given that each of the other bands is 10.5 cm wide,

So, the radius of 2^nd circle, r₂ = 10.5cm+10.5cm = 21 cm

Thus,

∴ Area of red region = Area of 2^nd circle − Area of gold region = (πr₂²−346.5) cm²

= (π(21)² − 346.5) cm²

= 1386 − 346.5

= 1039.5 cm²

Similarly,

The radius of 3^rd circle, r₃ = 21 cm+10.5 cm = 31.5 cm

The radius of 4^th circle, r₄ = 31.5 cm+10.5 cm = 42 cm

The Radius of 5^th circle, r₅ = 42 cm+10.5 cm = 52.5 cm

For the area of n^th region,

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

∴ 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

∴ 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

∴ 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