Solution:
Step 1:
We will calculate the volume of ice cream in the single scoop
The volume of the ice cream will be
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{2}{3}\pi r^3 \\ r=\frac{2in}{2}=1in(cone) \\ h=4.5in \\ r=\frac{3in}{2}=1.5in(radius\text{ of the hemisphere\rparen} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} V=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^{3} \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+\frac{2}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{14} \\ V=\frac{165}{14} \\ V=11.79in^3 \end{gathered}[/tex]Step 2:
We will use the formula below to calculate the volume of the two scoops of ic cream
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{4}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5in+\frac{4}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{7} \\ V=\frac{132}{7} \\ V=18.86in^3 \end{gathered}[/tex]Step 3:
We will use the formula below to calculate the volume of the three scoops of ic cream
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{6}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+2\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{297}{14} \\ V=\frac{363}{14} \\ V=25.93in^3 \end{gathered}[/tex]For the first ice cream with one scoop
[tex]\begin{gathered} 1in^3=\frac{3.50}{11.79} \\ 1in^3=\text{ \$}0.30 \end{gathered}[/tex]For the second ice cream with two scoops
[tex]\begin{gathered} 1in^3=\frac{4.50}{18.86} \\ 1in^3=\text{ \$}0.24 \end{gathered}[/tex]For the third ice cream with three scoops
[tex]\begin{gathered} 1in^3=\frac{5.50}{25.93} \\ 1in^3=\text{ \$}0.21 \end{gathered}[/tex]Hence,
The final answer is
The triple sold at $5.50 has the best value because it has the lowest price of $0.21 per cubic inch of the ice cream
