Two cubes each of volume 27 cm^{3} are joined end to end to form a solid. Find the surface area of the resulting cuboid.

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#### Solution

Let the edge of each cube be *a* cm.

Volume of each cube = *a*^{3} cm^{3}

It is given that the volume of each cube is 27 cm^{3}.

∴ *a*^{3} = 27= (3)^{3}

⇒ *a* = 3

Thus, length of each edge of the cube = 3 cm

When two cubes are joined end-to-end, the solid obtained is a cuboid whose length, breadth and height are 6 cm, 3 cm and 3 cm respectively.

This can be diagrammatically shown as follows:

Surface area of the cuboid = 2 (*lb* + *bh* + *hl*)

= 2 (6 cm × 3 cm + 3 cm × 3 cm + 3 cm × 6 cm)

= 2 × 45 cm^{2}

= 90 cm^{2}

Thus, the surface area of the resulting cuboid is 90 cm^{2}.

Concept: Surface Area of a Combination of Solids

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