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Three cubes of metal whose edges are 9, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube?

Correct answer: D. 18 cm

  • A. 21 cm
  • B. 19 cm
  • C. 32 cm
  • D. 18 cm

Explanation

Because the metal is melted without loss, the new cube's volume is the sum of the original volumes: 9 cm cubed + 12 cm cubed + 15 cm cubed = 729 cm3 + 1728 cm3 + 3375 cm3 = 5832 cm3. Since 18 cm x 18 cm x 18 cm = 5832 cm3, the new edge is 18 cm. Students may choose 21 cm, option a, by adding the three edge lengths rather than the 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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