Cone

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

Correct answer:

x =  23 dm

Step-by-step explanation:

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

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