Multiple choice

A circle of $5$ cm radius is drawn and another circle of $3$ cm radius is cut out of this circle. What is the radius of a circle which has the same area as the area of bigger circle excluding the cut one?

  1. $2$ cm
  2. $3$ cm
  3. $4$ cm
  4. $4.5$ cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Area of larger circle = pi * 5^2 = 25pi. Area of smaller circle = pi * 3^2 = 9pi. Remaining area = 25pi - 9pi = 16pi. New radius r satisfies pi * r^2 = 16pi, so r = 4.

AI explanation

Using the area of a circle formula, the area of the remaining region is pi * 5^2 - pi * 3^2 = 25 * pi - 9 * pi = 16 * pi square cm. Equating this to the area of a new circle with radius x gives pi * x^2 = 16 * pi. Solving for x yields x = 4 cm.

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