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# Fig. 12.3 depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.Q.3

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Today i am solving ncert class 10 chapter Areas Related To Circles it is very hard to solve exercise 12.1 question no. 3 please help me to solve this .Give me the best and easiest solution of this chapter. Fig. 12.3 depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions

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1. The radius of 1stÂ circle, r1Â = 21/2 cm (as diameter D is given as 21 cm)

So, area of gold region = Ï€ r12Â = Ï€(10.5)2Â = 346.5 cm2

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

So, the radius of 2ndÂ circle, r2Â = 10.5cm+10.5cm = 21 cm

Thus,

âˆ´ Area of red region = Area of 2ndÂ circle âˆ’ Area of gold region = (Ï€r22âˆ’346.5) cm2

= (Ï€(21)2Â âˆ’ 346.5) cm2

= 1386 âˆ’ 346.5

= 1039.5 cm2

Similarly,

The radius of 3rdÂ circle, r3Â = 21 cm+10.5 cm = 31.5 cm

The radius of 4thÂ circle, r4Â = 31.5 cm+10.5 cm = 42 cm

The Radius of 5thÂ circle, r5Â = 42 cm+10.5 cm = 52.5 cm

For the area of nthÂ region,

A = Area of circle n â€“ Area of circle (n-1)

âˆ´ Area of blue region (n=3) = Area of third circle â€“ Area of second circle

= Ï€(31.5)2Â â€“ 1386 cm2

= 3118.5 â€“ 1386 cm2

= 1732.5 cm2

âˆ´ Area of black region (n=4) = Area of fourth circle â€“ Area of third circle

= Ï€(42)2Â â€“ 1386 cm2

= 5544 â€“ 3118.5 cm2

= 2425.5 cm2

âˆ´ Area of white region (n=5) = Area of fifth circle â€“ Area of fourth circle

= Ï€(52.5)2Â â€“ 5544 cm2

= 8662.5 â€“ 5544 cm2

= 3118.5 cm2

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