The area of a circle got increased by 22 cm when the radius was increased by 1 cm. What was the original radius?Top
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A.
9 cm
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B.
5 cm
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C.
7 cm
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D.
3 cm
Correct Answer:
D. 3 cm
Explanation:
To determine the original radius of the circle, we can use the area formula A = πr².1. Let the original radius be r. The original area is πr².
2. If the radius increases by 1 cm, the new radius becomes (r + 1). The new area is π(r + 1)².
3. The problem states the area increased by 22 cm². Therefore: π(r + 1)² - πr² = 22.
4. Expanding the equation: π(r² + 2r + 1) - πr² = 22.
5. Simplifying: πr² + 2πr + π - πr² = 22, which leaves 2πr + π = 22.
6. Using the approximation π ≈ 22/7: 2(22/7)r + 22/7 = 22.
7. Multiply the entire equation by 7/22 to simplify: 2r + 1 = 7.
8. Solving for r: 2r = 6, so r = 3.The original radius was 3 cm. Based on the provided options, the correct answer is 3 cm (Option D).
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