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A cube is built using $64$ cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the body (in square units) after the removal is ________.

  1. $56$
  2. $64$
  3. $72$
  4. $96$
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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.
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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.

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the surface area of the body will remain unchanged as when a cube is removed, it exposes three faces, which makes the number of exposed faces same as before removal.
 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.

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