SOLUTION: Show that the volume of the frustum of a cone with top and bottom radii R and r respectively and height, h is V = ⅓πh(R² + Rr + r²)

Algebra ->  Test -> SOLUTION: Show that the volume of the frustum of a cone with top and bottom radii R and r respectively and height, h is V = ⅓πh(R² + Rr + r²)      Log On


   

Question 1161702: Show that the volume of the frustum of a cone with top and bottom radii R and r respectively and height, h is
V = ⅓πh(R² + Rr + r²)
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!





John

My calculator said it, I believe it, that settles it

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

For the formula itself, see this Wikipedia article

https://en.wikipedia.org/wiki/Frustum

It is interesting, that the formula was known in ancient Egypt and ancient Greece.



For its derivation, see this WEB-page

https://www.toppr.com/guides/maths/surface-areas-and-volumes/frustum-of-cone/#:~:text=Answer%3A%20Substituting%20the%20value%20of,R3%20%E2%80%93%20r3)%2Fr%5D.

Or use these keywords "derivation formula for volume of conic frustum" in Google search engine.


Have a nice day (!)