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
Solution:
Radius (r₁) of the gold region = 21/2 cm = 10.5 cm
Given that each circle is 10.5 cm wider than the previous circle.
Therefore, radius (r₂) of the 2nd circle = 10.5 cm + 10.5 cm = 21 cm
Radius (r₃) of the 3rd circle = 21 cm + 10.5 cm = 31.5 cm
Radius (r₄) of the 4 th circle = 31.5 cm + 10.5 cm = 42 cm
Radius (r₅) of the 5 th circle = 42 cm + 10.5 cm = 52.5 cm
Area of the gold region = Area of the 1st circle = πr₁2 = π (10.5)2 = 346.5 cm2
Area of the red region = Area of the 2nd circle - Area of the 1st circle
= πr₂2 - πr₁2
= π(21)2 - π(10.5)2 cm2
= (1386 - 346.5) cm2
= 1039.5 cm2
Area of blue region = Area of 3rdcircle - Area of 2ndcircle
= πr₃2 - πr₂2
= π(31.5)2 -π(21)2 cm2
= 992.25π - 441π cm2
= 551.25π cm2
= 1732.5 cm2
Area of black region = Area of 4thcircle - Area of 3rd circle.
= πr₄2 - πr₃2
= π(42)2 - π(31.5)2
= 1764π - 992.25π
= 771.75π
= 2425.5 cm²
Area of white region = Area of 5thcircle - Area of 4 thcircle
= πr₅2 - πr₄2
= π(52.5)2 - π(42)2
= 2756.25π - 1764π
= 992.25π
= 3118.5 cm²
Hence, areas of the gold, red, blue, black, and white regions are 346.5 cm2, 1039.5 cm2, 1732.5 cm2, 2425.5 cm2 and 3118.5 cm2 respectively.
☛ Check: NCERT Solutions for Class 10 Maths Chapter 12
Video Solution:
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
NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.1 Question 3
Summary:
If an archery target is marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White and the diameter of the region representing the Gold score is 21 cm and each of the other bands is 10.5 cm wide, the scoring areas of gold, red, blue, black, and white regions of archery targets are 346.5 cm2, 1039.5 cm2, 1732.5 cm2, 2425.5 cm2, and 3118.5 cm2 respectively.
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