# 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 2^{nd} circle = 10.5 cm + 10.5 cm = 21 cm

Radius (r₃) of the 3^{rd} 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 1^{st }circle = πr₁^{2} = π (10.5)^{2} = 346.5 cm^{2}

Area of the red region = Area of the 2^{nd }circle - Area of the 1^{st }circle

= πr₂^{2} - πr₁^{2}

= π(21)^{2} - π(10.5)^{2 }cm^{2 }

= (1386 - 346.5) cm^{2 }

= 1039.5 cm^{2 }

Area of blue region = Area of 3^{rd}circle - Area of 2^{nd}circle

= πr₃^{2 }- πr₂^{2}

= π(31.5)^{2} -π(21)^{2} cm^{2 }

= 992.25π - 441π cm^{2 }

= 551.25π cm^{2 }

= 1732.5 cm^{2 }

Area of black region = Area of 4^{th}circle - Area of 3^{rd} circle.

= πr₄^{2} - πr₃^{2}

= π(42)^{2} - π(31.5)^{2}

= 1764π - 992.25π

= 771.75π

= 2425.5 cm²

Area of white region = Area of 5^{th}circle - Area of 4 ^{th}circle

= πr₅^{2 }- πr₄^{2}

= 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 cm^{2}, 1039.5 cm^{2}, 1732.5 cm^{2}, 2425.5 cm^{2} and 3118.5 cm^{2} respectively.

**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 cm^{2}, 1039.5 cm^{2}, 1732.5 cm^{2}, 2425.5 cm^{2}, and 3118.5 cm^{2} respectively.