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

For the cone:

`\begin{gathered} V=(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`