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Asked by Ananya Last Modified
Answer 
Abhay
Radius (r1) of 1st circle = 8 cm
Radius (r2) of 2nd circle = 6 cm
Let the radius of 3rd circle be r.
Area of 1st circle 
Area of 2nd circle 
Given that,
Area of 3rd circle = Area of 1st circle + Area of 2nd circle
However, the radius cannot be negative. Therefore, the radius of the circle having area equal to the sum of the areas of the two circles is 10 cm.
Radius (r1) of gold region (i.e., 1st circle) 
Given that each circle is 10.5 cm wider than the previous circle.
Therefore, radius (r2) of 2nd circle = 10.5 + 10.5
21 cm
Radius (r3) of 3rd circle = 21 + 10.5
= 31.5 cm
Radius (r4) of 4th circle = 31.5 + 10.5
= 42 cm
Radius (r5) of 5th circle = 42 + 10.5
= 52.5 cm
Area of gold region = Area of 1st circle 
Area of red region = Area of 2nd circle − Area of 1st circle
Area of blue region = Area of 3rd circle − Area of 2nd circle
Area of black region = Area of 4th circle − Area of 3rd circle
Area of white region = Area of 5th circle − Area of 4th circle
Therefore, areas of gold, red, blue, black, and white regions are 346.5 cm2, 1039.5 cm2, 1732.5 cm2, 2425.5 cm2, and 3118.5 cm2 respectively.
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