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.
Solution:
False
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 x + x x 3 x )=2(3x2 + x2 + 3x2)
= 2 x 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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