Multiple choice

If the radius of a circle is increased by 1 cm, its area increases by 22 cm2, then the radius of the path of circle is

  1. 4 cm

  2. 3 cm

  3. 3.5 cm

  4. 5 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The increase in area is π[(r + 1)^2 - r^2] = π(2r + 1) = 22. Using π = 22/7 gives 2r + 1 = 7, so r = 3 cm.

AI explanation

Using the area of a circle formula, A = pi * r^2, the initial area is pi * r^2 and the new area becomes pi * (r + 1)^2. Expanding the new area gives pi * (r^2 + 2r + 1), so the increase is pi * (2r + 1). Setting this equal to the given increase of 22 cm2 and using pi as 22/7, we solve (22/7) * (2r + 1) = 22 to find 2r + 1 = 7, meaning the original radius is 3 cm.

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