Draw a side view of the figure. Using similar triangles, it is clear that
(9-h)/r = 9/6
h = 9 - 3r/2
Now we can compare volumes, and we find
1/3 pi * 6^2 * 9 = 9 pi r^2 h
108 = 9r^2(9 - 3r/2)
r^3 - 6r^2 + 8 = 0
r = 1.3054
A cone has diameter 12 and height 9. A cylinder is placed inside the cone so the base of the cylinder is concentric with the base of the cone and the upper base of the cylinder is contained in the surface of the cone. If the volume of the cone is nine times the volume of the cylinder, find the dimensions of the cylinder.
1 answer