The cores of three cubes are 8 cm, 6 cm and 1 cm respectively. Having

1.	The cores of three cubes are 8 cm, 6 cm and 1 cm respectively. Having melted these cubes a new cube is recastesd. Find the total surface area of the new cube recanted.
Answer» Volume of the cube with core of 8 cm = (core)³ = 8³ = 512 cm³ Volume of the cube with core 6 cm = (core)³ = (6)³ = 216 cm³. Volume of the cube with core 1 cm = (core)³ = (1)³ = 1 cm³. The total volume of three cubes 512 + 216 + 1 = 729 cm³. Having melted these cubes, a new cube is recasted ∴ The volume of the cube recasted = 729 cm³ ⇒ (core)³ = 729 ⇒ core = \(\sqrt [ 3 ]{ 729 } \) = (9³)^1/3 = 9 cm Total surface area of cuboid recasted =6 (core)² 6 × 9 × 9 = 486 cm². Hence the surface area of the new cube = 486 cm².

The cores of three cubes are 8 cm, 6 cm and 1 cm respectively. Having melted these cubes a new cube is recastesd. Find the total surface area of the new cube recanted.

Answer»

Volume of the cube with core of 8 cm = (core)³

= 8³ = 512 cm³

Volume of the cube with core 6 cm = (core)³

= (6)³ = 216 cm³.

Volume of the cube with core 1 cm = (core)³

= (1)³ = 1 cm³.

The total volume of three cubes 512 + 216 + 1 = 729 cm³.

Having melted these cubes, a new cube is recasted

∴ The volume of the cube recasted = 729 cm³

⇒ (core)³ = 729

⇒ core = \(\sqrt [ 3 ]{ 729 } \)

= (9³)^1/3 = 9 cm

Total surface area of cuboid recasted =6 (core)²
6 × 9 × 9 = 486 cm².

Hence the surface area of the new cube = 486 cm².