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Question
Two cubes, each of volume 512 cm3 are joined end to end. Find the surface area of the resulting cuboid.
Solution
\[\text { Two cubes each of volume 512 } {cm}^3\text { are joined end to end . }\]
\[\text { Now, volume of a cube = (side ) }^3 \]
\[ \Rightarrow 512 = \text { (side ) }^3 \]
\[ \Rightarrow\text { Side of the cube = }\sqrt[3]{512} = 8 cm \]
\[\text { If the cubes area joined side by side, then the length of the resulting cuboid is 2 } + \times 8 cm = 16 cm . \]
\[\text { Breadth = 8 cm } \]
\[\text { Height = 8 cm }\]
\[ \therefore \text { Surface area of the cuboid = 2 } \times\text { (length }\times \text { breadth + breadth } \times \text{ height + length } \times \text { height) }\]
\[ = 2 \times (16 \times 8 + 8 \times 8 + 16 \times 8)\]
\[ = 2 \times (128 + 64 + 128)\]
\[ = 640 {cm}^2\]
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