64 small identical cubes are used to form a large cube

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Hi! I did not understand why you did 4^2, and why 8 more cubes are required at the corners.

The 4^ 2 is because there are 4 cubes on one side of the face. A face has 4 sides ( which makes it a square), so one face has 4+4+4+4 = 16 cubes.
Then, there are 6 faces, so 16*6 = 96 cubes
There are also 4 cubes on each edge = 4*12= 48
and since there are 8 corners in a big cube ( 4 that you can see, 4 at the back, and one at the bottom that you cant see). If you draw a cube and try counting the edges you'll find 8 edges

64 small cube will make a large cube with 4 cubes in each line i.e.
Adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line.

Total number of small cubes in new cube = 6^3 = 216

Extra cube required = 216 - 64 = 152

Hence, C is the answer.

Smaller cube = 4 x 4 x 4

Larger cube possible = 6 x 6 x 6

Two sides = 6 * 6 * 2 = 72

Remaining 4 sides = 16 * 4 = 64

4 corners = 4 * 4 = 16

Total = 72 + 64 + 16 = 152

Let the side of the cube is x. The area is X^3=64 X=4 , there are 4 cubes on each side
To add one top layer of small cube all over the surface of the large cube.
we have to add one cube at both ends of a side 1+4+1=6, the new cube will have =216 cubes.

The difference in the number of cubes we've added: 216−64=152

C

Why you have mentioned 'area' where as you have calculated 'volume'?

Given 64 small cubes are used to form a large cube.

Consider the smaller cube with dimensions of 1 unit each. We get volume of each smaller cube = 1 cubic unit

The larger cube will have a volume = 64 cubic units = 4^3 cubic units.

Hence the larger cube has dimensions as 4 units & is made of 64 cubes.

Now if we want to add a top layer of cubes on each surface, hence we are increasing the dimensions of the larger cube by 1 unit in all directions.

Hence the height of the cube will be increased by 1 unit on the top & by 1 unit on the bottom. Similarly for length & width.

We get a new larger cube of dimensions 6 units. Its volume = 6^3 = 216 cubic units & is made of 216 cubes.

Therefore the no. of additional cubes required = 216 - 64 = 152 cubes


Answer C.


Thanks,
GyM

According to the Q, we have a cube stack of 4 at every axis of a 3d plane : 4^3=64
As we need to add 1 layer at each side we need a total stack of (1+4+1)^3 = 216 cubes
Thus , small cubes required to meet the cond : 216-64 =152.... Ans C

It's a 4 x 4 x 4 cube.

An extra layer will make it 6 x 6 x 6 cube (a cube on each side will increase each edge by 2 cubes)

Difference = 6^3 - 4^3 = 216 - 64 = 152

C is my answer.

simple math:
small cube+64 should be equals to larger cube , a number of cubic form.

so starting from option A 64*64 is not a cube number
proceeding direct to answer option,as i already sovled, 152+64=216=6^3,so solved.

ONE KUDO IF YOU LIKE THE METHOD.

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