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There are two circles of different radii. The area of a square is 196 sq.cm, whose side is half the radius of the larger circle. The radius of the smaller circle is three-seventh that of the larger circle. What is the circumference of the smaller circle ?

Correct answer: C. 24 π cm

  • A. 12 π cm
  • B. 16 π cm
  • C. 24 π cm
  • D. 32 π cm

Explanation

The square has side √196 sq.cm = 14 cm, and this is half the larger circle's radius, so the larger radius is 28 cm. The smaller radius is 3/7 x 28 cm = 12 cm. Its circumference is 2π x 12 cm = 24π cm. Option b comes from using the smaller radius as 8 cm by mishandling the ratio.

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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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