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The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube?

Correct answer: D. 6 dm

  • A. 3 dm
  • B. 4 dm
  • C. 5 dm
  • D. 6 dm

Explanation

The combined volume is 3^3 dm3 + 4^3 dm3 + 5^3 dm3 = 27 dm3 + 64 dm3 + 125 dm3 = 216 dm3. Since the new cube has edge e, e^3 = 216 dm3, so e = 6 dm. The common mistake is choosing 5 dm, the largest original edge, instead of conserving total 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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