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Question 3
Figure 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

Diameter of Gold circle (first circle) = 21 cm
Radius of first circle, r1=212cm=10.5 cm
Each of the other bands is 10.5 cm wide,
Radius of second circle, r2=10.5cm+10.5cm=21cm
Radius of third circle, r3=21cm+10.5cm=31.5cm
Radius of fourth circle, r4=31.5cm+10.5cm=42cm
Radius of fifth circle, r5=42cm+10.5cm=52.5cm
Area of gold region =πr21=π(10.5)2=346.5cm2
Area of red region = Area of second circle - Area of first circle
= πr22346.5cm2=π(21)2346.5cm2
= 1386346.5cm2=1039.5cm2
Area of blue region = Area of third circle - Area of second circle
=πr231386cm2=π(31.5)21386cm2
=3118.51386cm2=1732.5cm2
Area of black region = Area of fourth circle - Area of third circle
=πr233118.5cm2=π(42)21386cm2
=55443118.5cm2=2425.5cm2
Area of white region = Area of fifth circle - Area of fourth circle
= πr245544cm2=π(52.5)25544cm2
= 8662.55544cm2=3118.5cm2

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