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.

Question

State whether the statement are True or False.

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.

Answer 1

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.