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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