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Question

# Depicts an archery target marked with its five scoring regions from the center outwards as gold,red,blue,black and white. The diameter of the region representing gold score is 21cm and each of the other bands is 10.5cm wide. Find the area of each of the five scoring regions.

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Solution

## width of each circle l=150 cmcircle A:- diameter =k=21 cmcircle B ⇒ diametre =k+2l=42 cm=2kcircle C ⇒ diametre =k+4l=21×3 cm=3kcircle D ⇒ diametre =k+6l=21×4 cm=4kcircle 3 dimeter =k+8l=21×5 cm=5karea of gold region = area of circle A=πk24=224×21×214=346.5 cm2are of red region = area of circle B− area of circle A=π(2k)24−π(k)24=3xπk24=3346.5 cm2=1039.5 cm2area of blue region =areaofcircleC-areofcircleB\$=π(3k)24−π(2k)24=5×(πk24)=5×346.5 cm2=1732.5 cm2area of black region = are of circle D− area of circle C=π(4k)24−π(3k)24=3dfracπk24=7×346.5 cm2=2425.5 cm2area of white region = area of circle E− area of circle D=π(5k)24−π(4k)24=9πk24=9×346.5 cm2=3118.5 cm2∴ The area 346.5, 1039.5, 1732.5, 2425.5 and 3118.5 cm2 respectively

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