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If the perimeter of circle A is equal to perimeter of semi circle B, what is the ratio of their areas ?
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- (π + 2)² : 2π²
- 2π² : (π + 2)²
- (π + 2)² : 4π²
- 4π² : (π + 2)²
- (π + 2)² : 2π²
Correct Option: C
Let radius of circle A be r1 units.
Radius of semi-circle = r2 units.
According to the question, 2πr1 = πr2 + 2r2
⇒ 2πr1 = r2 (π + 2)
| ⇒ | = | |||
| r2 | 2π |
| ∴ Ratio of their areas = | = | = (π + 2)² : 4πr² | ||
| πr2² | (2π)² |
