Can anyone help me with this problem?

Question

Water is being poured into an inverted right circular conical container. If the diameter of the base is 10cm and the height is 20cm, express the volume of the water in the container as a function of it's depth

Answer 1

Volume for a cone is V = 1/3 π r^2 h

In a right circular cone, there is a constant relationship between radius (or diameter) and height.

The diameter is given as 10 cm and the height, 20 cm.

Therefore the radius is 5 cm and the radius is 1/4 of the height. This is true anywhere on the cone.

If r = 1/4 h

Then by substitution,

V = 1/3 π (1/4h)^2 h =. 1/3 π 1/16 h^2 h

V = 1/48 π h^3

Please note I have used the word height in lieu of depth.