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A paper is in a square form whose one side is 20 cm. Two semi circles are drawn on its opposites as diameters. If these semi circles are cut down what is the area of the remaining paper?

Correct answer: A. (400 - 100π) cm2</sup

  • A. (400 - 100π) cm2</sup
  • B. (400 - 2π) cm2</sup
  • C. (400 - 200π) cm2</sup
  • D. 200π cm2</sup

Explanation

Each semicircle has diameter 20 cm, so radius 10 cm; the two semicircles together form one circle of area π(10 cm)² = 100π cm². The remaining area is the square's 400 cm² minus this, giving (400 - 100π) cm². The likely wrong choice is (400 - 200π) cm², which counts the two semicircles as two full circles.

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Area measures the surface enclosed by two-dimensional figures, while volume measures the space occupied by three-dimensional solids. Problems use formulas for rectangles, triangles, circles, prisms, cylinders, cones, spheres, and composite figures, including unit conversion and the distinction between surface area, lateral area, and volume.

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