A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed from every corner ...

Question

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

Accepted Answer

96 square units We start with a 4x4x4 cube (64 unit blocks). The cube has 8 corners. Removing one unit-cube from each corner changes the surface area: each corner removal exposes 3 new faces but hides 3 old faces, so the net change per corner is zero. The original surface area of a 4x4x4 cube is 6 * 4^2 = 96 square units, which remains unchanged after corner removals.