GATE CS 2016 Set 1 Q.5 (GA Q.5): Spatial Aptitude

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 __________.

Official answer and solution

Official answer: D
From: Official GATE 2016 answer key

Solution

Compute the original surface area and examine the geometric effect of removing corner unit cubes.

A cube constructed from 64 unit cubic blocks has side length:

s = \sqrt[3]{64} = 4\text{ units}

The total surface area of the original $4 \times 4 \times 4$ cube is:

\text{Surface Area} = 6 \times s^2 = 6 \times (4)^2 = 6 \times 16 = 96\text{ square units}

Now consider the removal of a $1 \times 1 \times 1$ cube from each of the 8 corners:

A corner cube originally has 3 exterior exposed faces (area $3 \times 1 = 3$ ).
When this corner cube is removed, it leaves behind an indentation with 3 newly exposed interior faces (each of area $1 \times 1 = 1$ ).

Because 3 exposed faces are removed and exactly 3 new identical faces are exposed, the net change in surface area at each corner is $3 - 3 = 0$ .
Since this applies to all 8 corners, the total surface area remains unchanged at 96 square units.

Final answer

Common trap

Subtracting the exposed surface area of the 8 corner blocks without accounting for the newly revealed interior faces.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2016 Computer Science and Information Technology (CS) Session 1
Question: 5 of 65, printed as GA Q.5
Section: General Aptitude

Report an error in this question

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.

Question

Solution

Source