How many cubes measuring 2 units must be added to a cube measuring 8 units to form a cube measuring 12 units?

Question

How many cubes measuring 2 units on one side must be added to a cube measuring 8 units on one side to form a cube measuring 12 units on one side?

Answer 1

Volume of cube with 12 unit side=12*12*12=1728.......(1 cube)
Volume of cube with 08 unit side=08*08*08=0512.......(1 cube)
Volume of cube with 02 unit side=02*02*02=08............(x cubes)
Therefore,
1*1728=(1*512)+(x*8)
x=152
Ans is 152 number of cubes measuring 2 units of side.

Answer 2

Firstly, we will calculate the number of 2 unit cubes in a cube measuring 8 units
A cube of 8 units is made up of 4 x 4 x 4 = 64 cubes of 2 units
Secondly, we will calculate the number of 2 unit cubes in a cube measuring 12 units
A cube of 12 units is made up of 6 X 6 X 6 = 216 cubes of 2 units
Therefore, The answer will be : 216 - 64 = 152 cubes of 2 units