# Fig. 12.3 depicts

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

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

The cost of fenciRS Aggarwal - Mathematics