Question

A Sno-Cone at the carnival has the shape of a hemisphere on top of an inverted cone. What is the volume ofthe sno-cone if its radius is 4.9 ft and the height of the conical portion is 9 ft?

Answer 1

The volume of the sno-cone is the volume of the semi-sphere on the top plus the volume of the cone on the bottom. So:

For the semi-sphere:

$\begin{gathered} V_{ss}=\frac{4}{3}\cdot\pi\cdot r^3 \\ where \\ r=4.9 \\ V_{ss}=\frac{4}{3}\cdot\pi\cdot(4.9^3) \\ V_{ss}\approx492.8069788ft^3 \end{gathered}$

For the cone:

$\begin{gathered} V=\frac{1}{3}\pi r^2h \\ where \\ r=4.9ft \\ h=9ft \\ V_c\approx226.2889188ft^3 \end{gathered}$

Therefore, the total volume is:

$V=719.0958976ft^3$