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A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?

Correct answer: D. None of these

  • A. 45 cm
  • B. 18 cm
  • C. 90 cm
  • D. None of these

Explanation

Equating the volumes, (4/3)π(12 cm)^3 = π(16 cm)^2L. Thus L = [4 x 12^3 cm^3]/[3 x 16^2 cm^2] = 9 cm. Since 9 cm is not listed, option d is correct. Option b may result from an incorrect division of the sphere's volume.

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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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