guerrero25 wrote:

64 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?

A. 64

B. 128

C. 152

D. 216

E. 256

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

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