Question

Three cubes of the same metal, whose edges are 6, 8, 10 cm are meltedand formed into a single cube. Find the diagonal of the single cube.
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Answer 1

Answer: 12√2 cm

Step-by-step explanation:

Cube 1: V = 6³ = 216

Cube 2: V = 8³ = 512

Cube 3: V = 10³ = 1000

New Cube: V = 1728

1728 = s³

12 = s

So, each side of the new cube is 12 cm.

Use Pythagorean Theorem to find the length of the diagonal:

12² + 12² = diagonal²

144 + 144 = diagonal²

288 = diagonal²

√288 = diagonal

12√2 = diagonal