96-8=88?

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57 votes

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Cube is built using $64$ cubic blocks of side one unit. It means it is a $4\times 4\times 4$ Cube.

Surface area of each face $ = 4\times 4$ sq. units

And number of faces in a cube $= 6$, Thus total surface area $ = 6\times 4\times 4 = 96$ sq. units.

A cube contains $8$ corner pieces (containing $3$ visible sides), and if these are removed then inner ones are visible, So, When a corner piece is removed $3$ new faces of $1$ sq. unit are visible and thus removal doesn't change surface area.

Hence, Option $(D)$ is correct.

Surface area of each face $ = 4\times 4$ sq. units

And number of faces in a cube $= 6$, Thus total surface area $ = 6\times 4\times 4 = 96$ sq. units.

A cube contains $8$ corner pieces (containing $3$ visible sides), and if these are removed then inner ones are visible, So, When a corner piece is removed $3$ new faces of $1$ sq. unit are visible and thus removal doesn't change surface area.

Hence, Option $(D)$ is correct.

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9 votes

A cube is built with 64 blocks of 1 unit side. Hence each side will have surface area $4\times4= 16$ square units.

if we remove one block from each corner, the resulting surface area will reduce by 4 square units. Hence surface area of each side is 12 square units.

Total surface area of 6 sides is $12\times6= 72$. But removal of a block from each corner creates an surface area of 3 square units.

Since there are 8 corners, the total surface area becomes $72 +3\times8 = 96$.

Hence **answer is D**.

1 vote

**If 64 cubic blocks are used to make the cube, it must be 4 x 4 x 4 blocks**

So, surface area of the body before removal = surface area of the body after removal = 6 * side * side = 6 * 4 * 4 = 96.

Thus, D is the correct choice.