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Two cubes each of volume $27\ cm^{3} \ $are joined end to end to form a solid. Find the area of resulting cuboid.
Given: Two cubes and volume of each $27\ cm^{3}$.
What to do: to find the surface area of the resulting cuboid after joining the both given cubes end to end.
Solution: Let the length of the given cubes is $\displaystyle a$.
Here volume is given$\ 27\ cm^{3}$.
$\therefore a^{3} =27$
$\Rightarrow a=\sqrt[3] ( 27)$
$=\sqrt[3] ( 3\times 3\times 3)$
$=3\ cm$
$\because$ both cubes are of the same volume
$\therefore$ both cubes will have the same sides.
When they are joined end to end,
The length of the resulting cuboid will be doubled but height and breadth will remain the same.
$\therefore$ length of resulting cuboid, $l=3+3=6\ cm$
Breadth of the cuboid, $b=3\ cm$
Height of the cuboid, $h=3\ cm$
Surface area of the resulting cuboid,$A=2( lb+bh+hl)$
$=2( 6\times 3+3\times 3+3\times 6)$
$=2( 18+9+18)$
$=90\ cm^{2}$
Thus, the area of the resulting cuboid is $90\ cm^{2}$.
Updated on: 10-Oct-2022
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