Question

if I have a conical cup 24 inches across the top and 20 inches deep what is the height of the water when it fills half the volume of the cup?

Answer 1

what is the volume of the full cup?

Answer 2

it might help to recall that the volume of a cone is 1/3 the volume of its representative cylindar

Answer 3

\[V=\frac13B_ah_o\]
\[V/2=\frac16B_ah_o\]
\[\frac13 B'h'=\frac16B_ah_o\]
\[B'h'=\frac12B_ah_o\]
\[h'=\frac1{2B'}B_ah_o\]
hmm, might need to address the relationship between diameter and height to iron it out now