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Question

There is a thin metal plate of length and breadth 2M mm and 2K mm respectively. Its thickness is 1mm. ‘N’ number of plates are placed one on top of the other? What is the object formed and what is its volume in mm3 ?      



A

Cuboid, MKN

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B

Cuboid, 4MKN

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C

Sphere, 4MKN

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D

Cylinder, 2 MKN

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Solution

The correct option is C

Cuboid, 4MKN


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

Total thickness = Thickness of one plate × Number of plates

                             = 1 mm × N

                             = N mm

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

The area of one plate = Length × Breadth

                                        = 2M × 2K

                                        = 4MK mm2 

Area of each plate is same. The area (cross section) of object is constant throughout. 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. 

The above diagram shows how thin plates stacked together form a cuboid.

Area of plate has 2 dimensions(Length and Breadth). The 3rd dimension is thickness.   

Volume = Plate Area ×Thickness

               = 4MK × N mm3 = 4MKN mm3.


Mathematics

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