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If three cubes of copper, each with an edge 6 cm, 8 cm and 10 cm respectively are melted to form a single cube, then what is the diagonal of the new cube ? 

(a) 18.8 cm 

(b) 22.8 cm 

(c) 20.8 cm 

(d) 24.8 cm

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Best answer

(c) 20.8 cm

Let the edge of the single cube be ‘a’ cm. 

Then, total volume melted = Volume of cube formed 

⇒ (6)3 + (8)3 + (10)3 = a3 

⇒ a3 = 216 + 512 + 1000 = 1728 ⇒ a = 12 cm. 

∴ Diagonal of the new cube = \(\sqrt3\,a=(\sqrt3\times12)\) cm = 20.8 cm (approx.)

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