Math CentralQuandaries & Queries


Question from Danica:

What portion of the height from top that the cone be cut into two equal volume?

Hi Danica,

I can help get you started.

In my diagram the large cone has radius $r$ and height $h$ and the top part of the cone has radius $r_1$ and height $h_{1}.$ Your task is to determine the fraction $f = \large \frac{h_1}{h}.$


The triangles $ABC$ and $DBE$ are similar so

\[\frac{r_1}{r} = \frac{h_1}{h} = f.\]

Write back if you need more assistance,

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