A Cone Half Full
Consider a right circular cone with diameter
of 12 cm for the base and altitude of 16 cm. If the cone is held
with its vertex down and water placed into it until it is half
full, what is the depth of the water?
Hint?
There is a unique result for this problem.
Can you find more than one way to solve for the result?
- Calculate the full volume and solve for the
height and radius of a cone with half the volume.
- Find the depth x when a cone of radius r
and height h is half full of water? Use this general solution
to find the solution for this particular cone.
- Let k range from 0 to 1. Plot the depth of
water x as k goes from 0 to 1 for this cone. That is, find x
= f(k) and graph it.
x
k
Graph of x = f(k)
Thanks to Eghaghe Mike for suggesting this problem.
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