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2 cubes each of volume (64;cm^{3}) are joined end to end. Find the surface area of the resulting cuboid.

Question

2 cubes each of volume \(64\;cm^{3}\) are joined end to end. Find the surface area of the resulting cuboid.

Answer

\(160\ cm^2\)
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Solution

Given, the volume of a cube is \(64\;cm^{3}\).Let side of the cube is \(a\;cm\),then

\(a^{3}=64=4^{3}\)
 \(\Rightarrow \)\(a=4\;cm\)
When we join each cube end to end, then, length of the new cuboid become
\((4+4)=8\;cm\).
Width and Height of the cuboid is 4cm each.
\(\therefore \)The surface area of the resulting cuboid \(=2(lb+bh+hl)\)
\(=2(8\times 4+4\times 4+4\times 8)\)
\(=2(32+16+32)\)
\(=2(80)\)
\(=160\;cm^{2}\)
Hence, the total surface area of the cuboid is \(160cm^2\).
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