If three cubes of copper, each with an edge 6 cm, 8 cm and 10 cm respe

1.	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
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.)

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

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.)