As a project I am asked to derive the volume of a cone, square and cylinder using a cut out of the geometric figures. I have tried searching many websites, videos etc. but couldn't find it.

I am hoping that this website helps me find out how to derive it (the formula of volume) using a cut out of a cylinder, cone and square.

  • $\begingroup$ What shape is your cut-out? what can you measure? $\endgroup$ – Henry Apr 25 '18 at 17:16
  • $\begingroup$ umm it is a cone as of now. i really did not get your second question, i am sorry. $\endgroup$ – Harshashri Ramesh Apr 25 '18 at 17:30
  • $\begingroup$ Unroll the cone. $\endgroup$ – amd Apr 26 '18 at 0:15


Below, you can see the unrolled cone "the cut out to it" and the cone itself.

enter image description here

If you can measure $\alpha$ and $R$ (or directly the length of the arc on the cut out) then the key to the solution is that the circumference of the base circle of the cone equals the arc length measured. From the circumference, you can calculate $r$ and, also, from r and $R$ the height...


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