Question

In the figure given below depicts an archery target marked with its five scoring regions from the centre outwards was 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.

Answer 1

(i) The diameter of the region representing Gold Score : 21 

d = 21 cm. 

∴ Radius, r = \(\frac{21}{2}cm\)

∴ Area of the region representing Gold score = πr²

A = 346.5 sq. cm. 

(ii) Radius of the region representing Gold score and Red score: 

r = 10.5 + 10.5 = 21 cm. 

∴ Area of the region representing Red score: Area of the region representing Gold and Red Score — Area of the region representing Gold score. 

= πr2 – πr2

∴ A = 1039.5 sq.cm. 

(iii) Total radii of the region representing Gold, Red and Blue region : 

r =10.5 + 10.5 + 10.5 = 31.5 cm

= \(\frac{63}{2}\)cm

∴ Area of the region representing Blue region: 

[ Area of the region representing Gold, Red and Blue regions ] — Area of the region representing Gold and Red region 

∴ A = πr² – πr²

(iv) Similarly, to find Area of the region representing Black region : 

∴ A = πr² – πr²

∴ A = 2425.5 sq. cm. 

(v) Area of the region representing white: 

∴ A = πr² – πr²

∴ A = 3118.5 sq. cm