GATE CS 2016 Set 1 — Question 5
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General Aptitude → Quantitative Aptitude → 2D & 3D Patterns
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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 __________.
Correct answer
(D) 96
Solution
A cube built using 64 cubic blocks of side 1 unit forms a cube.
The initial surface area of the cube is square units.When a unit block is removed from a corner:
Since there are 8 corners, the total change is .Thus, the surface area remains square units.
The initial surface area of the cube is square units.When a unit block is removed from a corner:
1.Three faces of the corner block that were part of the surface are removed ( sq units).
2.However, removing the corner block exposes three inner faces of the adjacent blocks ( sq units).
The net change in surface area per corner removed is .Since there are 8 corners, the total change is .Thus, the surface area remains square units.
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