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Question
Two cubes each of volume 27 cm3 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 = a3 cm3
It is given that the volume of each cube is 27 cm3.
∴ a3 = 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 cm2
= 90 cm2
Thus, the surface area of the resulting cuboid is 90 cm2.
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