Question

Each side of a cube is 3 units. It is cut into cubes each of side 1 unit What is the total surface area of
the smaller cubes thus obtained?​

Answer 1

• We are given that each side of a cube is 3 units and we are cutting it into multiple cubes of side 1 unit each.
• We have to find total surface area of all such 1 unit cubes.
• So initial total volume = 3 * 3 * 3 units

        = 27 unit^3.

• And each small cube has total volume

       = 1 unit^3.

• So we have total 27 small cubes with total surface area of each cube

       = 6 * (side length)^2.

• So each small cube will have total surface area :

     = 6 unit^2.

• And so total surface area of all such small cubes:

     = 27 * 6 unit^2.

     = 162 unit^2.

Answer 2

Given :

The each side of cube = a = 3 units

The cube is cut into other cubes each of side = b = 1 unit

To Find :

Total surface area of  the smaller cubes

Solution :

Since , each side of bigger cube = a = 3 unit

So, Total surface area of bigger cube = 6 × a²

i.e  Total surface area of bigger cube = 6 × (3 unit)²

∴ Total surface area of bigger cube =  54 sq unit

And, Volume of bigger cube = a³

i.e                                             = ( 3 unit )³

Or, Volume of bigger cube = 27 cubic unit

Now,

The bigger cube is cut into smaller cube of side 1 unit

So, Volume of smaller cube = b³

i.e                                             = ( 1 unit )³

Or, Volume of smaller cube = 1 cubic unit

So, Number of smaller cube = $\dfrac{volume of bigger cube}{volume of smaller cube}$

Or,      n = $\dfrac{27unit^{3} }{1unit^{2} }$

∴   number of smaller cubes = 27

Again

Total surface area of smaller cubes = 6 × b²

                                                           =  6 × 1² = 6 sq unit

Total surface area of all 27 smaller cubes = total number of cubes × 1²

∴                                                         = 27 × 6

                                                          = 162  sq unit

Hence, Total surface area of all 27 smaller cubes is 162 sq unit  Answer