Question

Fig. 12.3 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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Answer 1

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r =Radius of the region representing Gold score = 10.5 cm

Radius 1 = Radius of the region representing Gold and Red scoring areas

= (10.5 +10.5) cm = 21 cm = 2r cm

Radius 2 = Radius of the region representing Gold, Red and Blue scoring areas

= (21 + 10.5) cm = 31.5 cm = 3r cm

Radius 3= Radius of the region representing Gold, Red, Blue and Black scoring areas

- (31.5 +10.5) cm = 42 cm = 4r cm

Radius 4 =Radius of the region representing Gold, Red, Blue, Black and white scoring areas

= (42 + 10.5) cm = 52.5 cm = 5r cm

Now,

A1 = Area of the region representing Gold scoring area

$= \pi \: {r}^{2} \\ </p><p> \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{22}{7} \times 1.5 \times 10.5 \\ = {346.5 \: cm \: }^{2}$

A2 = Area of the region representing Red scoring area

$= \pi \: {(2r)}^{2} - \pi \: {r}^{2} \\ = 3\pi \: {r}^{2} \\ = 3 \: area \\ = 3 \times 346.5 \\ = 1039.5 \: {cm}^{2}$

Similarly:-

A3= Area of the region representing Blue scoring area

$= 5 \times 346.5 \\ = 1732.5 \: {cm}^{2}$

A4 = Area of the region representing Black scoring area

$= 7 \times 346.5 \\ = 2425.5 \: {cm}^{2}$

A5 = Area of the region representing White scoring area

$= 9 \times 346.5 \\ = 3118.5 \: {cm}^{2}$

Answer 2

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