Commercial cloud kitchens are always busy. Food orders are received and delivered around the clock, but some parts of the day are busier than others.

During off-peak hours, chefs often expect kitchen workers to make time-saving preparations for food service with important tasks, such as equipment cleaning and utensil organizing.

**Soup ladles** (or ladles in general) are kitchen utensils that are used for the safe and sanitary transfer of liquids during food preparation and food service. Ladles are best described as bowls with long handles.

The size of each ladle bowl is usually standardized using the traditional (avoirdupois) fluid volume units, such as fluid ounces, cups or pints.

**New Vocabulary:**

Learn how to say the word **“avoirdupois”** by hearing the pronunciation on Google Translate.

Common measuring instruments, such as rulers and tape measures, use inches and centimeters, so measuring fluid ounces directly is not very intuitive.

A math solution must be developed to make length measurements more relatable to volumetric sizing.

## Sorting the soup ladles

You have been given a box full of soup ladles to organize for the kitchen chef. This is an important responsibility and an opportunity to impress your boss.

One of the keys to a successful kitchen is the amount of preparation for food service. Preparation time is designed to optimize cooking time.

**Timing is crucial in cooking. **If the ladles are well-organized during preparation time, then the chefs and cooks will require much less time and effort to choose the correct ladle while cooking.

There are no size labels on the soup ladles given to you, but there is a way to measure and confirm each ladle size. For this math practice activity, our strategy will be to measure the width (i.e., the diameter) of the soup ladle bowls in inches and convert that measurement into standardized units in fluid ounces.

## Finding fluid ounces from diameters

The shape of the soup ladle bowls are best described as hemispheres (half spheres). We are familiar with the formula for a sphere, so this is a good starting place for calculating the formula for half of a sphere.

**CCSS.MATH.CONTENT.HSG.GMD.A.3:** Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

The volume of a sphere can be described with the following equation:

Thus, the volume of a hemisphere is half that volume.

We can measure the *diameter D* of the soup ladle (in inches) with a measuring tape.

The *radius R* of the soup ladle is half the measured diameter (D/2). So, we can rewrite the equation of the hemisphere in terms of the diameter:

The *volume V* (in cubic inches) is now a function of the *diameter D*, as given by the formula for the volume of a hemisphere.

After the volume is calculated, the units of cubic inches can be can converted into fluid ounces by multiplying the volume by 0.554113.

Below is the Wolfram Alpha input for this developed math solution.

**Sample Wolfram Alpha input**`D=4.5;R=D/2; `

`V=((4/3)*pi*R^3)/2;`

`Z=V*0.554113`

Notice how we can build the math solution without needing to explicitly use substitutions. That is one of the many powerful features of Wolfram Alpha.

It is a good practice to do the computations by hand. However, Wolfram Alpha provides an extra tool – one of many math tools – in the workplace for working through your computational thinking.

Additionally, once you have developed a good workplace math solution, you can simply repeat the calculation for a variety of input values.

The following table provides a list of standardized soup ladle sizes. Your calculations do not exactly match the these sizes, but they are close enough to help you finish the sorting task that the chef has assigned to you.

# Soup Ladle Diameters and Sizes

Diameter, D (in.) |
Volume, V (fl. oz.) |
Size (fl. oz.) |
---|---|---|

2 | 1.16 | 1 |

2.5 | 2.27 | 2 |

3.25 | 4.98 | 4 |

3.5 | 6.22 | 6 |

4 | 9.28 | 8 |

4.5 | 13.22 | 12 |

5 | 18.13 | 16 |

**NOTE: **Markdown tables were generated with Google Sheets using MarkdownTableMaker, another Bitwise Thermodynamics project.

## Conclusion

With more math practice, you will discover that the unit volume (e.g., cubic inches, cubic centimeters, etc.) provides a convenient way for you to convert between various workplace measurement systems.

Let us say you were tasked with buying new soup ladles for banquet service. The product descriptions may use gallons, quarts, or pints to describe different volumes. Calculating * price per cubic inch* is a useful method of comparison shopping based on a single variable.

**MathForWork** delivers distributed learning systems, instruction support, and test preparation for all learners. Learn more at MATHFORWORK.COM. MathForWork is a Bitwise Thermodynamics project.