472.

Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm are melted and a new cube is made (i) Find the length of the edge of the new cube.
(ii) Find the total surface area of the new cube.

Let the edges of the cubes of metal be a, b and c respectively, then
a = 6 cm, b = 8 cm and c = 10 cm
and thus respective volumes are,
v₁ = (6)³, V₂ = (8)³ and V₃ = (10)³
Now, the volume of new cube
= V₁ + V₂ + V₃
= 6³ + 8³ + 10³
= 1748 = 12³ cm³.
Let the length of the edge of the new cube be = a cm, then
a³ = 12³ ⇒ a = 12 cm.
(ii) The total surface area of the new cube
= 6a² = 6 x 12 x 12
= 864 cm².