The volume of a cone is given by the formula V = (1/3)πr²h, where "V" is the volume of the cone, "r" is the radius of the base, and "h" is the height of the cone.
If the cone is exactly half full of water by volume, then the volume of water is equal to half the volume of the cone. Let's call this volume "Vw".
So, Vw = (1/2) V
Substituting the formula for the volume of a cone, we get:
(1/3)πr²h(water) = (1/2) (1/3)πr²h(cone)
Simplifying, we get:
h(water) = (1/2) h(cone)
Therefore, the depth of the water in the cone is half the height of the cone.