Which Shape Holds the Most? (Volume of Solid Figures)

Introduction

Mathematics – Grade 6
Topic: Volume of Solid Figures (Cube, Rectangular Prism, Cylinder, and Cone)

Imagine you have been hired by a packaging company to help design the best container for storing drinks. The company wants to know which shape can hold the most liquid while using a practical design. Should they use a cube, a rectangular prism, a cylinder, or a cone?

As a Volume Investigator, your mission is to research different containers used in everyday life, calculate their volumes, and determine which shape is the most efficient. By the end of this WebQuest, you will discover how mathematics helps engineers and product designers make important decisions.

Task

Working in groups of 3–4 students, you will investigate the volumes of different three-dimensional containers.

Your group will:

  • Research four real-life containers (cube, rectangular prism, cylinder, and cone).
  • Record each container's dimensions from reliable online sources.
  • Calculate the volume of each container.
  • Compare the capacities of the containers.
  • Recommend which shape is the most efficient for holding liquids and explain your reasoning using mathematical evidence.

Final Product:

  • A comparison table of the containers
  • Complete volume calculations
  • A short presentation (3–5 minutes)
  • A written recommendation identifying which container holds the most and why

Process

Step 1 – Learn About Volume

Visit the recommended websites to review the formulas for finding the volume of solid figures.

As you learn, answer these questions:

  • What is volume?
  • Why is volume important?
  • What units are used to measure volume?

Step 2 – Research Real Containers

Each group member researches one of the following container shapes:

  • Cube (e.g., storage box)
  • Rectangular Prism (e.g., milk or juice carton)
  • Cylinder (e.g., soda can)
  • Cone (e.g., paper cone cup)

Record:

  • Name of the container
  • Length, width, height, or radius (as needed)
  • Source of the measurements
     

Step 3 – Calculate the Volume

Using the appropriate formulas, calculate the volume of each container.

  • Cube
  • Rectangular Prism
  • Cylinder
  • Cone

Show all computations clearly.

Step 4 – Compare the Results

Create a comparison table including:

  • Container shape
  • Dimensions
  • Formula used
  • Calculated volume
  • Rank from largest to smallest volume

Discuss:

  • Which shape holds the most?
  • Which shape is commonly used for beverages?
  • Why might companies choose one shape over another?

Step 5 – Present Your Findings

Prepare a 3–5 minute presentation explaining:

  • Your research process
  • The volume calculations
  • Which container holds the most
  • Your recommendation supported by mathematical evidence

Evaluation

Evaluation

Criteria Excellent (10) Good (8) Fair (6) Needs Improvement (4)
Research and Data Collection Gathered complete, accurate information from reliable online sources. Information is mostly complete with minor omissions. Some information is missing or inaccurate. Very limited or inaccurate research.
Accuracy of Volume Calculations All formulas and calculations are correct and clearly shown. Minor computational errors that do not affect most results. Several errors in formulas or calculations. Most calculations are incorrect or incomplete.
Comparison Table and Analysis Comparison table is complete, organized, and includes clear analysis of results. Table is complete with minor errors or limited analysis. Table is incomplete or analysis lacks detail. Table is missing or difficult to understand.
Recommendation and Mathematical Justification Recommendation is logical, well-supported by mathematical evidence, and clearly explained. Recommendation is supported with some mathematical evidence. Recommendation has limited explanation or evidence. Recommendation is unclear or unsupported.
Presentation and Teamwork Presentation is well-organized, engaging, and all members actively participate. Presentation is organized and most members participate. Presentation lacks organization or participation is uneven. Presentation is incomplete or minimal teamwork is shown.

Total Score: 50 points

Grading Scale

45–50 points – Outstanding

38–44 points – Very Good

30–37 points – Satisfactory

Below 30 points – Needs Improvement

Conclusion

Congratulations, Volume Investigators!

Through this WebQuest, you discovered that different three-dimensional shapes can hold different amounts even when they appear similar in size. By researching real containers and applying volume formulas, you learned how mathematics helps engineers, manufacturers, and designers choose the best packaging for products. The next time you see a milk carton, soda can, or ice cream cone, you'll understand the mathematical thinking behind its design.

Credits

Resources

Students may use the following educational and reference websites:

Teacher Page

Which Shape Holds the Most?
A WebQuest on the Volume of Solid Figures

Mathematics – Geometry

Unit of Study: Volume of Solid Figures (Cube, Rectangular Prism, Cylinder, and Cone)

Overview

This WebQuest engages students in an inquiry-based investigation of the volume of common three-dimensional containers. Working collaboratively, students research real-life objects, calculate their volumes using appropriate mathematical formulas, compare the capacities of different shapes, and make evidence-based recommendations about the most efficient container for holding liquids.

Through this activity, students discover how geometry is applied in everyday life, particularly in packaging, engineering, and product design.

Learning Objectives

By the end of this WebQuest, students will be able to:

  • Calculate the volume of cubes, rectangular prisms, cylinders, and cones using the correct formulas.
  • Apply mathematical concepts to real-life objects and situations.
  • Compare and analyze the capacities of different solid figures.
  • Interpret data and justify conclusions using mathematical evidence.
  • Conduct online research using reliable sources.
  • Collaborate effectively to solve problems and communicate findings.

Prerequisite Knowledge

Students should already be able to:

  • Measure length using metric units.
  • Use basic multiplication and division.
  • Identify common three-dimensional figures.
  • Substitute values into mathematical formulas.
  • Use calculators appropriately.

Materials Needed

  • Computer, tablet, or smartphone with Internet access
  • Calculator
  • Notebook or worksheet
  • Graph paper (optional)
  • Presentation software (PowerPoint, Google Slides, or Canva)

Suggested Websites

Students may use the following resources:

  • Math is Fun – Volume of 3D Shapes
  • Khan Academy
  • CK-12 Foundation
  • SplashLearn
  • Online shopping websites or manufacturer websites for product dimensions

Teachers may also provide printed measurements if internet access is limited.

Teacher's Role

During the WebQuest, the teacher serves as a facilitator rather than a lecturer by:

  • Guiding students in locating reliable online resources.
  • Helping students select appropriate formulas.
  • Monitoring group collaboration.
  • Providing support when students encounter mathematical difficulties.
  • Encouraging students to justify their conclusions using evidence rather than guesses.
  • Leading a class discussion after presentations to reinforce key concepts.

Assessment

Student learning will be assessed using the WebQuest rubric based on:

  • Research and data collection
  • Accuracy of volume calculations
  • Comparison table and analysis
  • Mathematical reasoning and recommendation
  • Presentation and teamwork

Total Score: 50 points

Reflection

After completing the activity, encourage students to reflect on the following questions:

  • Which container shape surprised you the most? Why?
  • How did mathematics help you compare different containers?
  • Where else do you think volume is important in everyday life?
  • What was the biggest challenge your group encountered, and how did you overcome it?

Expected Learning Outcomes

Upon completing this WebQuest, students should demonstrate not only proficiency in calculating the volume of solid figures but also an understanding of how geometry is used in everyday decision-making. They should be able to apply mathematical reasoning, interpret data, communicate their findings effectively, and appreciate the practical value of mathematics in designing and comparing real-world objects.