Question

In a particular country, the value of a diamond is directly proportional to the surface area (exposed) of the diamond. Four thieves steal a cubical diamond piece and then divide equally into four parts. What is the maximum percentage increase in the value of diamond after cutting it?

• A. 50%
• B. 66.66%
• C. 100%
• D. None of these

Answer 1

The correct option is C 100%

To increase the value (or price of diamond), they should cut (divide) the diamond in such a way that the surface area will be maximum.


Thus, when four parts are parallel to each other.
In this way, total surface area
$=6a^2+2a^2+2a^2+2a^2=12a^2$
Actual surface area of cubical diamond = $6a^2$
Therefore, percentage increase in area
$=\frac{12a^2-6a^2}{6a^2}\times 100=100\%$
Remember that for the given volume, the minimum surface area is possessed by a cube. So to maximize the area we have to increase the maximum possible difference between the edges of the cuboid.