Question : Three cubes of iron whose edges are 6 cm, 8 cm, and 10 cm, respectively, are melted and formed into a single cube. The edge of the cube formed is:
Option 1: 12 cm
Option 2: 14 cm
Option 3: 16 cm
Option 4: 18 cm
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Correct Answer: 12 cm
Solution : Given: The edges of three cubes are 6 cm, 8 cm, and 10 cm. Let the edge of the unknown cube be a. According to the question, Volume of the 1st cube + Volume of the 2nd cube + Volume of the 3rd cube = Volume of the large cube ⇒ 6 3 + 8 3 + 10 3 = a 3 ⇒ a 3 = 216 + 512 + 1000 ⇒ a 3 = 1728 $\therefore$ a = 12 Hence, the correct answer is 12 cm.
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