Question
Fig. 12.3, depicts an archery target marked with its five scoring areas 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.
Fig. 12.3
Solution
We have,
r = Radius of the region representing Gold score = 10.5 cm
∴ r1 = Radius of the region representing Gold and Red scoring areas = (10.5 + 10.5) cm = 21 cm = 2r cm
r2 = Radius of the region representing Gold, Red and Blue scoring areas = (21 + 10.5) cm = 31.5 cm = 3r cm
r3 = Radius of the region representing Gold, Red, Blue and Black scoring areas = (31.5 + 10.5) cm = 42 cm = 4r cm
r4 = Radius of the region representing Gold, Red, Blue, Black and white scoring areas = (42 + 10.5) cm = 52.5 cm = 5r cm
Now, A, = Area of the region representing Gold scoring area
= 22 × 1.5 × 10.5 = 346.5 cm2
A2 = Area of the region representing Red scorring area
= π (2r)2 - πr2 = 3πr2 = 3A1
= 3 × 346.5 cm2 = 1039.5 cm2
A3 = Area of the region representing Blue scoring area
= π(3r)2 - π(2r)2 = 9πr2 - 4πr2
= 5πr2 = 5A1 = 5 × 346.5 cm2
= 1732.5 cm2
A4 = Area of the region representing black scoring area
= π(4πr)2 - π(3r)2 = 7πr2 = 7A1
=7 × 346.5 cm2 = 2425.5 cm2
A1 = Area of the region representing white scoring area
= π(5r)2 - π(4r)2 - 9πr2 = 9 A1
= 9 × 346.5 cm2 = 3118.5 cm2
