Multiple choice

The area of shaded region between a square of side $14\ cm$ and the circle touching all sides of the square is

  1. $196\ cm^{2}$
  2. $42\ cm^{2}$
  3. $154\ cm^{2}$
  4. $350\ cm^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Area of square = 14 * 14 = 196. The circle touching all sides has a diameter of 14, so radius = 7. Area of circle = (22/7) * 7 * 7 = 154. Shaded area = 196 - 154 = 42.

AI explanation

The radius of the circle is half the side of the square, which is 14 divided by 2, equaling 7 cm. The area of the square is 14 squared, which is 196 sq cm, and the area of the circle is pi times r squared, or 22 over 7 times 49, equaling 154 sq cm. Subtracting the circle's area from the square's area gives 196 minus 154, resulting in a shaded region of 42 sq cm.

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