Q. 34.0( 453 Votes )

Fig. 12.3 depicts

Answer :

Radius (r1) of gold region (i.e., 1st circle) = = 10.5 cm

Given:


Each circle is 10.5 cm wider than the previous circle.


Hence,


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 1stcircle


= πr12


= π (10.5)2


= 346.5 cm2


Area of red region = Area of 2nd circle - Area of 1stcircle


= πr22 – πr12


= π (21)2 – π (10.5)2


= 441π – 110.25π


= 330.75π


= 1039.5 cm2


Area of blue region = Area of 3rdcircle - Area of 2ndcircle


= πr32 – πr22


= π (31.5)2 – π (21)2


= 992.25 π - 441 π


= 551.25 π


= 1732.5 cm2


Area of black region = Area of 4thcircle - Area of 3rd circle


= πr42 – πr32


= π (42)2 – π (31.5)2


= 1764 π – 992.25 π


= 771.75 π


= 2425.5 cm2


Area of white region = Area of 5thcircle - Area of 4thcircle


= πr52 – πr42


= π (52.5)2 – π (42)2


= 2756.25 π - 1764 π


= 992.25 π


= 3118.5 cm2


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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