A big cube painted with yellow colour in all sides. if you
cut it into 1000 cubes with same dimension. than how many
cubes were without painted anyside. explain it?

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A big cube painted with yellow colour in all sides. if you cut it into 1000 cubes with same dimens..

firstly,1000 cubes together makes a cube.
Cube=Side*Side*Side
therefore, side is equal to 10 units. (10*10*10=1000)

when the big cube is painted only the outer sides are
painted on thier outer side. therefore if we find out the
area of the each side, we can easily find out unpainted
cubes.

area=side*side (i.e. 10*10=100 units)

a cube has 6 sides, therefore 100*6=600 units.

therefore unpainted cubes are 1000-600=400

 Is This Answer Correct ? 112 Yes 42 No

A big cube painted with yellow colour in all sides. if you cut it into 1000 cubes with same dimens..

The big cube have 1000 small cube, so it's easy to know that
each edge have 10 piece (10*10*10 = 1000)
The big cube is painted in all sides so pieces in the core of
big cube won't be painted. So to answer "how many cubes were
without painted anyside." we just count how many cube in core
of original big cube. Imagine we remove the cover (created
from one layer of small cube) from big cube, we will have a
core cube which have each edge 8 small pieces
=> the answer = 8*8*8 = 512

 Is This Answer Correct ? 65 Yes 8 No

A big cube painted with yellow colour in all sides. if you cut it into 1000 cubes with same dimens..

Ans : 488

6x10X10 = 600 (Area for 6 faces )

common cubes counted twice in above calculation = 12x10 = 120
common cubes counted thrice and deducted trice in above
calculation = 8
so , 600 -120 +8 = 488

alternate method:
-------------------

10x10 + 10x10 + 8x10 + 8x10 + 8x8 + 8x8 = 488

 Is This Answer Correct ? 13 Yes 10 No

A big cube painted with yellow colour in all sides. if you cut it into 1000 cubes with same dimens..

A big cube painted with yellow colour in all sides. if you
cut it into 1000 cubes with same dimension. than how many
cubes were without painted anyside. explain it?

Hey if the cube is cutted into two cubes , the colour will not be in the cutted side of the cube. So If it is cutted into 1000 cubes. Then the answer is 1000 cubes were without painted any side.

 Is This Answer Correct ? 4 Yes 5 No

A big cube painted with yellow colour in all sides. if you cut it into 1000 cubes with same dimens..

100

 Is This Answer Correct ? 1 Yes 3 No

A big cube painted with yellow colour in all sides. if you cut it into 1000 cubes with same dimens..

the cubes which doesnt have any colour can be called as a "CORE CUBE"
as we have 1000 small cubes, and as its a 3 D one, i can say there are 10 pieces in each dimension (10*10*10=1000)
we have a formula to find it,

(n-2)^3

n= no of pieces in each dimension,

10-2)^3
=8^3
=516

 Is This Answer Correct ? 0 Yes 2 No

A big cube painted with yellow colour in all sides. if you cut it into 1000 cubes with same dimens..

If suppose we have a cube which is painted and cut into 27 pieces we have 1 pieces in the core which is not painted at all.(we have 9 pieces on each face)
Similarly when we have 16 pieces cut from a big cube by analyzing we have 8 pieces in the core which is not painted.
when we take a cube which is painted and cut into 8 pieces a simple example we have 0 pieces in the core.
so by generalizing we have a formula n3-(n-2)3
we take n=2; 8-0=8 painted face.
n=3 we have 27-1=26; 26 painted cubes.
n=4 we have 64-8=56;

thus for n=10,
1000-512=488

 Is This Answer Correct ? 2 Yes 5 No

A big cube painted with yellow colour in all sides. if you cut it into 1000 cubes with same dimens..

Where by giving one cut we can get two cubes so now divide
1000 by 2 will get 500..

 Is This Answer Correct ? 1 Yes 4 No

A big cube painted with yellow colour in all sides. if you cut it into 1000 cubes with same dimens..

it is evident that each side is of 10*10
so out of six sides if i remove upper and lower side then remaining is 1000-(2*100)=800
now that i have removed lower and upper side each side will be of (9*10) which is 4*(90)=360
therefore 800-360=440

 Is This Answer Correct ? 0 Yes 3 No

A big cube painted with yellow colour in all sides. if you cut it into 1000 cubes with same dimens..

there are 508 cubes which are not painted on any of the sides.

the cube has 6 sides.
If the cube is divided into 1000 cubes, then every side will show 100 sides of the small cubes.
Remember that the cubes on the edges share faces with more than one side of the big cube.

Every side of the big cube has 100 sides of the smaller cubes out of which 36 are on the edges and share sides with other sides of the big cube.
so remove all the cubes which are on the edges.
i.e. 1000-(36+26+26+10+10)= 892

now consider the inner faces that are painted, each side of the big cube is left with 64 sides of the small cubes.
so 892-(64*6)= 508

 Is This Answer Correct ? 1 Yes 5 No

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