A solid is in the form of a cone with vertical height \( h \) that is mounted on the top base ...

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A solid is in the form of a cone with vertical height \( h \) that is mounted on the top base of a right circular cylinder with height \( \frac{1}{3} \mathrm{~h} \). The circumference of the base of the cone and that of the cylinder are both equal to \( c \). If \( v \) be the volume of the solid, prove that
\[
c=\sqrt{\frac{6 \pi v}{h}}
\]
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