Multiple choice

A paper is in the form of a rectangle $ABCD$ where $AB = 22\ cm$ and $BC = 14\ cm$. A semi-circular portion with $BC$ as diameter is cut off. Find the area of the remaining part. $\left(Use\ \displaystyle \pi =\dfrac{22}{7} \right)$

  1. $130$ $\displaystyle cm^{2} $
  2. $231$ $\displaystyle cm^{2} $
  3. $200$ $\displaystyle cm^{2} $
  4. $441$ $\displaystyle cm^{2} $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of the rectangle is 22 * 14 = 308 cm^2. The semi-circle has a diameter of 14 cm, so the radius is 7 cm; its area is (1/2) * (22/7) * 7 * 7 = 77 cm^2. The remaining area is 308 - 77 = 231 cm^2.

AI explanation

The area of the rectangular paper is length times width, which is 22 cm multiplied by 14 cm, yielding 308 square cm. The area of a semi-circle is given by (1/2) * pi * r^2, where the radius is half of the diameter BC, so r = 7 cm. The semi-circular area is (1/2) * (22/7) * 7^2 = 77 square cm. Subtracting this removed portion from the total rectangle gives 308 - 77, resulting in a remaining area of 231 square cm.

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