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The edges of three iron cubes are 6cm; 8cm; 10cm respectively. A new cube was made by melting them. Find the edge of the new cube?

Correct answer: B. 12 cm

  • A. 8 cm
  • B. 12 cm
  • C. 14 cm
  • D. 10 cm

Explanation

The total volume of the melted cubes is 6³ cm³ + 8³ cm³ + 10³ cm³ = 216 cm³ + 512 cm³ + 1000 cm³ = 1728 cm³. Since 1728 cm³ = 12³ cm³, the new cube has edge 12 cm. The likely wrong choice is 10 cm, which treats the new edge as one of the original edges instead of combining volumes.

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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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