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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.
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Solution
\[\text { Three cubes of edges 3 cm, 4 cm and 5 cm are melted and molded to form a new cube } . \]
\[\text { i . e . , volume of the new cube = sum of the volumes of the three cube }s\]
\[ = (3 )^3 + (4 )^3 + (5 )^3 \]
\[ = 27 + 64 + 125\]
\[ = 216 {cm}^3 \]
\[\text { We know that volume of a cube = (side ) }^3 \]
\[ \Rightarrow 216 = \text { (side ) }^3 \]
\[ \Rightarrow \text {Side of the new cube = } \sqrt[3]{216} = 6 cm\]
\[ \therefore \text { Surface area of the new cube = 6 }\times\text { (side } )^2 = 6 \times (6 )^2 = 216 {cm}^2\]
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