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 5.5 mm and the height of the conical portion is 9.7 mm?

Answer 1

Answer:

Volume = 655.73

Explanation:

The sno-cone is composed of a hemisphere and a cone; therefore, its volume is

$V=V_{cone}+V_{hemisphere}$

Now

$V_{\text{cone}}=\frac{\pi r^2h}{3}$

and the volume of the hemisphere is

$V_{\text{hemisphere}}=\frac{2}{3}\pi r^3$

Therefore,

$V=V_{cone}+V_{hemisphere}$$\rightarrow V=\frac{\pi r^2h}{3}+\frac{2}{3}\pi r^3$

putting in h = 9.7 mm and r = 5.5 mm gives

$\begin{gathered} V=\frac{\pi(5.5)^2(9.7)}{3}+\frac{2}{3}\pi(5.5)^3 \\ \end{gathered}$

which simplifies to give (rounded to the nearest hundreth)

$V=655.73\operatorname{mm}^3$

which is our answer!