How many small cubes each of 96 cm2 surface area can be formed from th

1.	How many small cubes each of 96 cm2 surface area can be formed from the material obtained by melting a larger cube of 384 cm2 surface area ?
Answer» Let the edge of the bigger cube be a cm and the edge of the smaller cube be b cm. Then, 6a² = 384 and 6b² = 96 ⇒ a² = 64 and b² = 16 ⇒ a = 8 cm and b = 4 cm ⇒ Volume of bigger cube = a³ = (8)³ cm³ = 512 cm³ and Volume of smaller cube = b³ = (4)³ cm³ = 64 cm³. ∴ Total number of smaller cubes = \(\frac{512}{64}\) = 8.

How many small cubes each of 96 cm2 surface area can be formed from the material obtained by melting a larger cube of 384 cm2 surface area ?

Answer»

Let the edge of the bigger cube be a cm and the edge of the smaller cube be b cm.

Then, 6a² = 384 and 6b² = 96

⇒ a² = 64 and b² = 16

⇒ a = 8 cm and b = 4 cm

⇒ Volume of bigger cube = a³ = (8)³ cm³ = 512 cm³ and

Volume of smaller cube = b³ = (4)³ cm³ = 64 cm³.

∴ Total number of smaller cubes = \(\frac{512}{64}\) = 8.