The surface area of a cuboid formed by joining two cubes of side ' $a$ ' face to face is __________.

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Solution

The surface area of a cuboid formed by joining two cubes of side ' $a$ ' face to face is __________.

Let ' $a$ ' be the side of each cube.

When the two cubes are joined face to face, the figure obtained should be a cuboid having the same breadth and height. As the combined cube has a length twice the length of a cube.
It means that
$l = 2 a$
$b = a$
$h = a$
Hence, the total surface area of cuboid $=$ $2 (l b + b h + h l)$
Total surface area of cuboid $=$ $2 (2 a \times a + a \times a + a \times 2 a)$
Simplify the above expression, we get
$=$ $2 (2 a^{2} + a^{2} + 2 a^{2})$
$=$ $2 (5 a^{2})$
$=$ $10 a^{2}$ .
Hence, the required surface area of the cuboid is $10 a^{2}$ .

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