Question

Three cubes whose edges measure 3 cm, 4 cm, and 5 cm respectively are melted to form a new cube. Find the surface area of the new cube formed.

Answer 1

\[\text { Three cubes of edges 3 cm, 4 cm and 5 cm are melted and molded to form a new cube } . \]

\[\text { i . e . , volume of the new cube = sum of the volumes of the three cube }s\]

\[ = (3 )^3 + (4 )^3 + (5 )^3 \]

\[ = 27 + 64 + 125\]

\[ = 216 {cm}^3 \]

\[\text { We know that volume of a cube = (side ) }^3 \]

\[ \Rightarrow 216 = \text { (side ) }^3 \]

\[ \Rightarrow \text {Side of the new cube = } \sqrt[3]{216} = 6 cm\]

\[ \therefore \text { Surface area of the new cube = 6  }\times\text {  (side } )^2 = 6 \times (6 )^2 = 216 {cm}^2\]