SOLUTION: find the volume of a solid with circular base of radius r, if every plane perpendicular to a given diameter is a square.

Algebra ->  Volume -> SOLUTION: find the volume of a solid with circular base of radius r, if every plane perpendicular to a given diameter is a square.      Log On


   

Question 1178424: find the volume of a solid with circular base of radius r, if every plane perpendicular to a given diameter is a square.
Found 2 solutions by Solver92311, ikleyn:
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!



If the solid has a circular base, then it is a cone or a cylinder. Since the intersection of a plane perpendicular to a given diameter of the base and the solid is a square, then the solid must be a right circular cylinder, and furthermore, the height must be equal to the measure of a diameter. That is to say .

The formula for the volume of a right circular cylinder is:



Substitute for and simplify.

John

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

From
I > Ø

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

Surely, and it is OBVIOUS, that the solid in this problem is NOT A CYLINDER,


so the solution by other tutor is incorrect.


I don't know what is the correct solution to this problem.