Question

There is a thin coin of radius 2K mm and thickness 1 mm. Now I place M coins one on top of the other. What is the object formed and what is its volume?

• A. Cylinder, 2$\pi K^2$ $m{m}^3$
• B. Cuboid, 4$\pi K^2$ $m{m}^3$
• C. Sphere , 2$\pi M{K}^2$ $m{m}^3$
• D. Cylinder, 4$\pi M{K}^2$ $m{m}^3$

Answer 1

The correct option is D

Cylinder, 4$\pi M{K}^2$ $m{m}^3$

The sectional area of one coin = $\pi$$r^2$

= $\pi$$(2k{)}^2$

= 4$\pi$$k^2$ $m{m}^2$

The object we have here is a 2-D circle having the $3^{rd}$ dimension of thickness. A circle with height/thickness is nothing but a cylinder. When coins are stacked together we can get a taller cylindrical column. This can be represented below.

The volume of the cylinder = Area of circular section × Height/Thickness of one coin × Number of coins
= 4$\pi$$K^2$ × 1 × M

= 4$\pi$M$k^2$$m{m}^3$