Mathematics
Three cubes, whose edges are x cm, 8 cm and 10 cm respectively, are melted and recast into a single cube of edge 12 cm. Find 'x'.
Mensuration
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Answer
Given:
Edges of three cubes:
Cube 1: s1 = x cm
Cube 2: s2 = 8 cm
Cube 3: s3 = 10 cm
Edge of the new cube formed from the melted material = 12 cm
Total Volume of the Three Cubes = V1 + V2 + V3
⇒ s13 + s23 + s33 = S3
⇒ x3 + 83 + 103 = 123
⇒ x3 + 512 + 1,000 = 1,728
⇒ x3 + 1,512 = 1,728
⇒ x3 = 1,728 - 1,512
⇒ x3 = 216
⇒ x =
⇒ x = 6 cm
Hence, x = 6 cm.
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