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The volume of a cuboid is $l \times b \times h$. That is, it is equal to base area times height. I think it means that the base is added up height times, it becomes volume (It makes sense if we think about it)
And if we think about cylinder, the above mentioned logic still holds. The volume of cylinder is $\pi r^2 \times h$ . Which is same as saying the area of bottom circle (i.e. $\pi r^2$) times the height $h$.
But when it comes to a cone , it doesn't makes sense. In above examples 2-d shapes have been collected one upon another, a specific number of times(h). In a cone its kinda same except that now a triangle isn't collected one upon another (that would make a prism), but collected in a circular way. We can imagine a cone to be group of right triangles with their axis being one of the sides (except hypotenuse, that would make a compound shape of two cones ). We can also imagine it this way, A right triangle is rotated with one of the sides being axis.
So now the volume should be, by above mentioned logic, the area of repeated shape times number of shapes. And there are 2pi x r triangles because, well, it is rotated that much number of times. Visualize it in your mind, it'll become clear. Hope you get the idea.
Now, Volume of cone should be area of the triangle times the circumference of the base
=> $1/2 \times b \times h \times 2\pi r$
Now the base of triangle is same as the radius of the base and the 2s cancel each other out we are left with
$\pi r^2 h$
But the volume of cone if one third of that value. My question is Why is that?