Question

There is a thin metal plate of length and breadth 2M mm and 2K mm respectively. Its thickness is 1 mm. ‘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

Each plate has a thickness of 1 mm. When many plates are put together, the total thickness will be the sum of thickness of all the plates.

$\therefore \text{Total thickness = Thickness of one plate}\times \text{Number of plates}$
$=1mm\times N=Nmm$

The object formed has now 3 dimensions- Length, breadth and thickness.

$\text{The area of one plate}$
$=\text{Length}\times \text{Breadth}$
$=2M\times 2K$
$=4MKm{m}^2$
Now, if we multiply this area by the thickness/height we will get the Volume of object. The object formed when thin plates are stacked together is nothing but a cuboid. This can visualised as shown below.



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