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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 __________.
 
(A)   56 (B)   64 (C)   72 (D)   96
asked in Gate Papers by gatefoum

3 Answers

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(D)   96
answered by gatefoum
If 64 cubic blocks are used to make the cube, it must be 4 x 4 x 4 blocks.The surface area is 6 x 4 x 4 = 96 sq units.
Now picture this...each corner block shows off three faces. When it is removed, three new faces are exposed, thus there appears no net change in the exposed surface area...
96 sq. units
0 votes

If 64 cubic blocks are used to make the cube, it must be 4 x 4 x 4 blocks.
The surface area is 6 x 4 x 4 = 96 sq units.
Now picture this...each corner block shows off three faces. When it is removed, three new faces are exposed, thus there appears no net change in the exposed surface area...
96 sq. units

answered by IITLocked
0 votes

 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.
 
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.

answered by Saurav

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