Answer :

Radius (*r _{1}*) of gold region (i.e., 1st circle) = = 10.5 cm

Given:

Each circle is 10.5 cm wider than the previous circle.

Hence,

Radius (*r _{2}*) of 2nd circle = 10.5 + 10.5

21 cm

Radius (*r _{3}*) of 3rd circle = 21 + 10.5= 31.5 cm

Radius (*r _{4}*) of 4th circle = 31.5 + 10.5= 42 cm

Radius (*r _{5}*) of 5th circle = 42 + 10.5= 52.5 cm

Area of gold region = Area of 1^{st}circle

= πr1^{2}

= π (10.5)^{2}

= 346.5 cm^{2}

Area of red region = Area of 2nd circle - Area of 1^{st}circle

= πr_{2}^{2} – πr_{1}^{2}

= π (21)^{2} – π (10.5)^{2}

= 441π – 110.25π

= 330.75π

= 1039.5 cm^{2}

Area of blue region = Area of 3^{rd}circle - Area of 2^{nd}circle

= πr_{3}^{2} – πr2^{2}

= π (31.5)^{2} – π (21)^{2}

= 992.25 π - 441 π

= 551.25 π

= 1732.5 cm^{2}

Area of black region = Area of 4^{th}circle - Area of 3rd circle

= πr_{4}^{2} – πr_{3}^{2}

= π (42)^{2} – π (31.5)^{2}

= 1764 π – 992.25 π

= 771.75 π

= 2425.5 cm^{2}

Area of white region = Area of 5^{th}circle - Area of 4^{th}circle

= πr_{5}^{2} – πr_{4}^{2}

= π (52.5)^{2} – π (42)^{2}

= 2756.25 π - 1764 π

= 992.25 π

= 3118.5 cm^{2}

Therefore, areas of gold, red, blue, black, and white regions are 346.5 cm^{2}, 1039.5 cm^{2}, 1732.5 cm^{2}, 2425.5 cm^{2}, and 3118.5 cm^{2} respectively

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