Cone

Circular cone with height h = 29 dm and base radius r = 3 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume.

Correct result:

x =  23 dm

Solution:

$$\begin{gathered} {V}^{\mathrm{\prime }}={\displaystyle \frac{1}{2}}V \\ {\displaystyle \frac{1}{3}}\pi ({\displaystyle \frac{x\cdot r}{h}}{)}^2\cdot x={\displaystyle \frac{1}{6}}\pi r^2\cdot x \\ x=29\cdot {\displaystyle \frac{1}{\sqrt[3]{2}}}=23\text{ dm} \end{gathered}$$

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