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Question
The surface area of a cuboid formed by joining face to face 3 cubes of side x is 3 times the surface area of a cube of side x.
Options
True
False
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Solution
This statement is False.
Explanation:
Three cubes having side x are joined face-to-face, then the cuboid so formed has the same height and breadth as the cubes but its length will be thrice that of the cubes.
Hence, the length, breadth and height of the cuboid so formed are 3x, x and x, respectively.
Then, its surface area = 2(lb + bh + hl)
= 2(3x × x + x × x + x × 3x )
= 2(3x2 + x2 + 3x2)
= 2 × 7x2
= 14x2
Now, the surface area of the cube of side x = 6 (Side)2 = 6x2.
Hence, the statement is false.
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