Find the volume of the largest right circular cone that can be inscribed in a
sphere of radius 2.
Below is a picture that represents
the cross section of a cone (triangle) inscribed in a sphere (circle).
Drag the labeled point to change the
radius and height of the cone.
You may choose to show or hide either
curve.
The blue curve represents the graph
of the relation between the volume of the cone and its radius.
The red curve represents the graph of
the volume of the cone as a function of its height.
- Can you estimate the radius of the cone that will yield the largest
volume?
- Can you estimate the height of the cone that will yield the largest
volume?
- What is the approximate maximum volume?
This is a prototype of JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright ©1990-1998 by Key Curriculum Press, Inc. All rights reserved. Portions of this work were funded by the National Science Foundation (awards DMI 9561674 & 9623018).