Question

Question 55

State whether the following statement is 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)
$=2(3x\times x+x\times x+x\times 3x)=2(3x^2+x^2+3x^2)$
$=2\times 7x^2=14x^2$
Now, the surface area of the cube of side x $=6(Side{)}^2=6x^2$ Hence, the statement is false.