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.

Result

x =  23 dm

Solution:

 V′=12V 13π(x⋅rh)2⋅x=16πr2⋅x  x=29⋅123=23 dm \ \\ V' = \dfrac{1}{2} V \ \\ \dfrac{1}{3} \pi ( \dfrac{ x \cdot r }{h})^2 \cdot x = \dfrac{1}{6} \pi r^2 \cdot x \ \\ \ \\ x = 29\cdot \dfrac{1}{ \sqrt[3]{2}}= 23 \ \text{dm}

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