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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

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Solution

## Let r1, r2, r3, r4 and r5 be the radii of the gold, red, blue, black and white regions, respectively.Gold regiond1=2r1=21 cm∴r1=212 cmA1=πr12=π(212)2=441π4 cm2=4414×227 cm2=632×11 cm2=6932 cm2=346.5 cm2Hence, area of gold region =346.5 cm2Red regionr2=r1+10.5=212+212=21 cmA2=πr22=π(21)2=227×441 cm2=22×63 cm2=1386 cm2Hence, area of red region =A2−A1=1039.5 cm2Blue regionr3=r2+10.5=21+10.5=31.5 cmA3=πr32=π(31.5)2=227×992.25 cm2=21829.57 cm2=3118.5 cm2Area of blue region =A3−A2=1732.5cm2Black regionr4=r3+10.5=31.5+10.5=42 cmA4=πr42=π(42)2=227×1764 cm2=22×252 cm2=5544 cm2Hence, area of black region =A4−A3=2425.5 cm2White regionr5=r4+10.5=42+10.5=42.5 cmA5=πr52=π(42.5)2=227×1806.25 cm2=39737.57 cm2=8662.5 cm2Hence, area of white region =A5−A4=3118.5 cm2

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