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The radius of a wire is decreased to one -third if volume remains the same length will increase

Correct answer: D. 9 times

  • A. 1 Time
  • B. 3 times
  • C. 6 times
  • D. 9 times

Explanation

For a wire, volume is cross-sectional area x length, so pi x r^2 x L remains constant. Reducing the radius to r/3 makes the area (r/3)^2 = r^2/9, so the length must become 9L. The likely wrong choice is 3 times, which changes the length inversely with radius instead of with the square of the radius.

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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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