Question

There is a thin metal plate of length and breadth 2M mm and 2K mm respectively. Its thickness is 1 mm. If ‘N’ number of plates are placed one on top of the other, what is the object formed and what is its volume in $m{m}^3$?

• A. Cuboid, MKN
• B. Cuboid, 4MKN
• C. Sphere, 4MKN
• D. Cylinder, 2 MKN

Answer 1

The correct option is B Cuboid, 4MKN

Thickness of 1 plate = 1 mm.
Total thickness of N plates put together = N mm
The object formed has now 3 dimensions- Length, breadth and thickness.
The area of one plate
$=Length\times Breadth$
$=2M\times 2K$
$=4MKm{m}^2$
The object formed when thin plates are stacked together is nothing but a cuboid. This can be visualised as shown below.


$Volume=PlateArea\times Totalthickness$
$=4MK\times N$
$=4MKNm{m}^3$

[Note that, if $M=K=\frac{1}{2}$, then length, breadth and thickness are equal and hence the resulting solid will be a cube. But cube is a special case of cuboid. So, the given answer is correct in this case too.]