Fig. 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

Question

Fig. 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

Filo · Accepted Answer

Let r1​, r2​, r3​, r4​ and r5​ be the radii of the gold, red, blue, black and white regions, respectively.Gold regiond1​=2r1​=21cm∴r1​=221​ cmA1​=πr1​2=π(221​)2=4441π​ cm2\mbox {A(Gold region)} = 346.5 cm^2Red regionr2​=r1​+10.5=221​+221​=21cmA2​=πr2​2=π(21)2=1386cm2 \mbox{A(Red region)} = A_2-A_1 = 1039.5cm^2Blue regionr3​=r2​+10.5=21+221​=263​cmA3​=πr3​2=π(263​)2=3118.5cm2 \mbox{A(Blue region)} = A_3-A_2 = 1732.5cm^2Black regionr4​=r3​+10.5=263​+221​=42cmA4​=πr4​2=π(42)2=5544cm2 \mbox{A(Black region)} = A_4-A_3 = 2425.5cm^2White regionr5​=r4​+10.5=42+221​=2105​cmA5​=πr5​2=π(2105​)2=8662.5cm2 \mbox{A(White region)} = A_5-A_4 = 3118.5 cm^2

Question Text	Fig. 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 $21 c m$ and each of the other bands is $10.5 c m$ wide. Find the area of each of the five scoring regions
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Fig. 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 $21 c m$ and each of the other bands is $10.5 c m$ wide. Find the area of each of the five scoring regions

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