Chapter 4, Problem 22RE

Explanation of Solution

To find volume of cocktail shaker:

• A cocktail shaker consists of three cone sections.
• One cone section consists of radius “${\text{r}}_{\text{1}}$”, radius “${\text{r}}_2$”, and height “h”.
• The formula to find volume “V” for one cone section is as follows

  $\text{V=}\frac{\text{π}\left({\text{r}}_{\text{1}}{}^{\text{2}}\text{+r}\text{r}{}_{\text{2}}{\text{+r}}_{\text{2}}{}^{\text{2}}\right)\text{h}}{\text{3}}$

• For cone section 1, consider the values “0.3” inches for “${\text{r}}_{\text{11}}$”, “0.5” inches for “${\text{r}}_{\text{21}}$”, and “0.75” inches for “${\text{h}}_{\text{1}}$”, where “${\text{r}}_{\text{11}}$” indicates the first radius for first cone section, “${\text{r}}_{\text{21}}$” indicates the second radius for first cone section, and “${\text{h}}_{\text{1}}$” is the height of first cone section.
• For cone section 2, consider the values “0.5” inches for “${\text{r}}_{\text{12}}$”, “0.75” inches for “${\text{r}}_{22}$”, and “0.3” inches for “${\text{h}}_2$”, where “${\text{r}}_{12}$” indicates the first radius for second cone section, “${\text{r}}_{\text{22}}$” indicates the second radius for second cone section, and “${\text{h}}_2$” is the height of second cone section.
• For cone section 3, consider the values “0.75” inches for “${\text{r}}_{\text{13}}$”, “0.5” inches for “${\text{r}}_{\text{23}}$”, “3.0” inches for “${\text{h}}_3$”, where “${\text{r}}_{\text{13}}$” indicates the first radius for third cone section, and “${\text{r}}_{23}$” indicates the second radius for third cone section, and “${\text{h}}_3$” is the height of third cone section.
• To get the volume of the cocktail shaker, the volume of three cone sections need to be added.
• Therefore, the formula to find the volume “${\text{V}}_{\text{c}}$”of cocktail shaker is as follows

  ${\text{V}}_{\text{c}}{\text{=V}}_{\text{1}}{\text{+V}}_{\text{2}}{\text{+V}}_{\text{3}}$        (1)

  Where, “${\text{V}}_{\text{1}}$” is the volume of first cone section, “${\text{V}}_2$” is the volume of second cone section, “${\text{V}}_3$” is the volume of third cone section.

• The formula to find the volume for first cone section is as follows

  ${\text{V}}_1\text{=}\frac{\text{π}\left({\text{r}}_{\text{11}}{}^{\text{2}}\text{+r}\text{r}{}_{\text{21}}{\text{+r}}_{\text{21}}{}^{\text{2}}\right){\text{h}}_1}{\text{3}}$        (2)

• Substitutes the values “0.3” inches for “${\text{r}}_{\text{11}}$”, “0.5” inches for “${\text{r}}_{\text{21}}$”, and “0.75” inches for “${\text{h}}_{\text{1}}$” in Equation (2),

$\begin{array}{c}{\text{V}}_{\text{1}}=\frac{3.14({0.3}^2+0.3\times 0}{}\end{array}$

Explanation of Solution

Algorithm for computing volume of cocktail shaker:

Step-1: Assign the values for first radius, second radius, and height for each cone sections.

Step-2: Compute the volume for first cone section using the formula is as follows

${\text{V}}_1\text{=}\frac{\text{π}\left({\text{r}}_{\text{11}}{}^{\text{2}}\text{+r}\text{r}{}_{\text{21}}{\text{+r}}_{\text{21}}{}^{\text{2}}\right){\text{h}}_1}{\text{3}}$

Where, “${\text{r}}_{\text{11}}$” indicates the first radius, “${\text{r}}_{\text{21}}$” indicates the second radius, and “${\text{h}}_{\text{1}}$” is the height of first cone section.

Step-3: Compute the volume for second cone section using the formula is as follows

${\text{V}}_2\text{=}\frac{\text{π}\left({\text{r}}_{\text{12}}{}^{\text{2}}\text{+r}\text{r}{}_{\text{22}}{\text{+r}}_{\text{22}}{}^{\text{2}}\right){\text{h}}_2}{\text{3}}$

Where, “${\text{r}}_{12}$” indicates the first radius, “${\text{r}}_{\text{22}}$” indicates the second radius, and “${\text{h}}_2$” is the height of second cone section