• MAFS.8.G.3.9 : Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
  

• MAFS.8.G.3.AP.9a : Using a calculator, apply the formula to find the volume of three-dimensional shapes (i.e., cubes, spheres and cylinders).

• Volume of Spherical Bubble Tea: Learn how to calculate the volume of spheres while learning how they make Bubble Tea in this interactive tutorial.

• Sugar Cone: Students are asked to solve a problem that requires calculating the volume of a cone.

• Platinum Cylinder: Students are asked to solve a problem that requires calculating the volume of a cylinder.

• Louvre Pyramid: Students are asked to find the height of a square pyramid given the length of a base edge and its volume.

• Cylinder Formula: Students are asked to write the formula for the volume of a cylinder, explain what each variable represents, and label the variables on a diagram.

• Cone Formula: Students are asked to write the formula for the volume of a cone, explain what each variable represents, and label the variables on a diagram.

• Burning Sphere: Students are asked to solve a problem that requires calculating the volume of a sphere.

• Sphere Formula: Students are asked to write the formula for the volume of a sphere, explain what each variable represents, and label the variables on a diagram.

• Pyramid Formula: Students are asked to write the formula for the volume of a pyramid, explain what each variable represents, and label the variables on a diagram.

• What Floats Your Boat: Students will solve real-world and mathematical problems involving density. Students will engineer solutions to the given problem using gained scientific content knowledge as application of mathematical skills

• Slope Intercept - Lesson #1: This is lesson 1 of 3 in the Slope Intercept unit. This lesson introduces graphing proportional relationships. In this lesson students will perform an experiment to find and relate density of two different materials to the constant of proportionality and unit rate.

• Knight Shipping, Inc.: In this design challenge students will take what they have learned about calculating the volumes and densities of cones, cylinders, and spheres, to decide which shape would make the best shipping container. Students will calculate the volumes and densities to help select the best design and then test them to move at least 3 containers of the chosen shape across the classroom. Students will fill the shapes with marshmallows to visually confirm which shape would hold more.

• How Many Cones Does It Take?: This lesson is a "hands-on" activity. Students will investigate and compare the volumes of cylinders and cones with matching radii and heights. Students will first discover the relationship between the volume of cones and cylinders and then transition into using a formula to determine the volume.

• Find your Formula!: Use this discovery lesson to introduce the volume of pyramids and cones. The class is divided into two groups: one for pyramids and one for cones. One group compares the volume of a pyramid to a prism, and the other group compares the volume of a cone to a cylinder with the same radius and height. Using the investigation results, students write the volume formulas for both a pyramid and a cone.

• Silly Cylinders: This is a short activity where students determine the density of the human body by considering each part of the body to be a cylinder. I use this activity during the second week of school, so students have already had some practice with measurement. In addition to providing students with practice in data collection and problem solving, it is a good activity that allows teachers to measure students' previous knowledge in these areas.

• Area to Volume Exploration: In this student-centered lesson, the formulas for the volume of a cylinder, cone, and a sphere are examined and practiced. The relationship between the volume of a cone and a cylinder with the same radius and height is explored. Students will also solve real-world problems involving these three-dimensional figures.

• Modeling Volume: Making Matchsticks: This lesson deepens students’ understanding of volume by engaging them in multiple problem-solving strategies. Students begin by tackling an open-ended volume problem independently. They then analyze and critique three different sample solutions, each demonstrating a unique approach. To support instruction, the lesson includes teacher prompts and background information designed to guide students’ thinking and promote meaningful discussion.

• Pack It Up: Students use geometry formulas to solve a fruit growing company's dilemma of packing fruit into crates of varying dimensions. Students calculate the volume of the crates and the volume of the given fruit when given certain numerical facts about the fruit and the crates.

  Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

• Victorious with Volume: Students explore the relationship between the volume of cylinders and cones.

• Mix & Match Soup: Using paper, soup cans, and chocolate candies, students explore how to find the volume of a cylinder by making connections with circles and various real-world items.

• Relating Surface Area and Volume: Students will recognize that while the surface area may change, the volume can remain the same. This lesson is enhanced through the multimedia CPALMS Perspectives Video, which introduces students to the relationship between surface area and volume.

• Velocity of the Aucilla River: Harley Means discusses the mathematical methods hydrologists use to calculate the velocity of rivers.

  Download the CPALMS Perspectives video student note taking guide.

• Carbon Foam and Geometry: <p>Carbon can take many forms, including foam! Learn more about how geometry and the Monte Carlo Method is important in understanding it.</p>

• Unit Rate and Florida Cave Formation: How long does it take to form speleothems in the caves at Florida Caverns State Parks?

  Download the CPALMS Perspectives video student note taking guide.

• Volume and Surface Area of Pizza Dough: Michael McKinnon of Gaines Street Pies explains how when making pizza the volume is conserved but the surface area changes.

• Mathematically Optimizing 3D Printing: <p>Did you know that altering computer code can increase 3D printing efficiency? Check it out!</p>
• KROS Pacific Ocean Kayak Journey: Food Storage Mass and Volume: What do you do if you don't have room for all your gear on a solo ocean trek? You're gonna need a bigger boat...or pack smarter with math.

  Related Resources:
  KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
  KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]

  Download the CPALMS Perspectives video student note taking guide.

• Glasses: In this resource, students will determine the volumes of three different shaped drinking glasses. They will need prior knowledge with volume formulas for cylinders, cones, and spheres, as well as experience with equation solving, simplifying square roots, and applying the Pythagorean theorem.

• Comparing Snow Cones: Using the context of an ice cream shop, students will compare the volumes of a cone and a truncated cone (the cone on the bottom is removed) to determine the percent increase in volume.

• Flower Vases: The purpose of this task is to give students practice working the formulas for the volume of cylinders, cones and spheres, in an engaging context that provides and opportunity to attach meaning to the answers.

• Shipping Rolled Oats: Students will think of different ways the cylindrical containers can be arranged in a rectangular box. Through the process, students should realize that although some setups may seem different, they result in a box with the same volume. In addition, students should come to the realization (through discussion and/or questioning) that the thickness of a cardboard box is very thin and will have a negligible effect on the calculations.

• Cylinder Volume and Surface Area: This video demonstrates finding the volume and surface area of a cylinder.

• Volume of a Sphere: This video shows how to calculate the volume of a sphere.

• Volume of a Cone: This video explains the formula for volume of a cone and applies the formula to solve a problem.

• Three Dimensional Shapes: In this interactive, self-guided unit on 3-dimensional shape, students (and teachers) explore 3-dimensional shapes, determine surface area and volume, derive Euler's formula, and investigate Platonic solids. Interactive quizzes and animations are included throughout, including a 15 question quiz for student completion.