Water was poured into a cone with a volume of 32 to the middle of the height. What is the volume of water?

The volume of the cone is determined by the formula:

V = 1/3 * π * H * R ^ 2, where H is the height, R is the radius.

R ^ 2 = 3 * V / π * H

The generator L is easy to find by the Pythagorean theorem:

L ^ 2 = H ^ 2 + R ^ 2.

The height of the small cone will be: h = H / 2.

Small radius square: r = 1/4 * (H ^ 2 + R ^ 2) – H ^ 2/4 = R ^ 2/4.

The volume Vs filled with liquid will be equal to the difference between the volumes of these cones:

Vs = V – v = V – 1/3 * π * h * r ^ 2 = V -1/3 * π * H / 2 * 3 * V / π * H = V -V / 2 = 32 – 16 = 16.