SOLUTION: find the volume of a solid with circular base of radius r, if every plane perpendicular to a given diameter is a square.
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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) (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(52810) (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.
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