Fig. 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.

Let r1, r2, r3, r4 and r5 be the radii of the gold, red, blue, black and white regions, respectively.

Gold region
d1 = 2r1 = 21 cm
∴r1 = 21/2 cm
A1 = πr1² = π(21/2)² = 441π/4 cm² = 441/4 × 22/7 cm² = 63 × 11 cm² = 693/2 cm² = 346.5 cm²
Hence, area of gold region = 346.5 cm²

Red region
r2 = r1 + 10.5 = 21/2 + 21/2 = 21 cm
A2 = πr2² = π(21)² = 22/7 × 441 cm² = 22 × 63 cm² = 1386 cm²
Hence, area of red region = A2 − A1 = 1039.5 cm²

Blue region
r3 = r2 + 10.5 = 21 + 10.5 = 31.5 cm
A3 = πr3² = π(31.5)² = 22/7 × 992.25 cm² = 22/7 × 992.25 cm² = 3118.5 cm²
Area of blue region = A3 − A2 = 1732.5 cm²

Black region
r4 = r3 + 10.5 = 31.5 + 10.5 = 42 cm
A4 = πr4² = π(42)² = 22/7 × 1764 cm² = 22 × 252 cm² = 5544 cm²
Hence, area of black region = A4 − A3 = 2425.5 cm²

White region
r5 = r4 + 10.5 = 42 + 10.5 = 52.5 cm
A5 = πr5² = π(52.5)² = 22/7 × 2756.25 cm² = 8662.5 cm²
Hence, area of white region = A5 − A4 = 3118.5 cm²