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# Volume

## Explore several methods for finding the volume of objects, using both standard cubic units and non-standard measures. Explore how volume formulas for solid objects such as spheres, cylinders, and cones are derived and related.

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### In This Session

Part A: How Many Cubes?
Part B: Volume Formulas
Homework

Volume is literally the “amount of space filled.” But on a practical level, we often want to know about capacity — how much does a container hold? — so we often measure volume as the number of units it takes to “fill the object.” Visualizing and counting three-dimensional arrays of cubes is at the core of understanding volume.

We measure volume using both liquid measures (e.g., milliliters, deciliters, and liters; pints, quarts, and gallons) and solid measures (e.g., cubic centimeters, cubic decimeters, and cubic meters; cubic inches, cubic feet, and cubic yards). Note 1 In this session we will focus primarily on measuring volume using solid measures.

For information on required and/or optional materials in this session, see Note 2.

### Learning Objectives

In this session, you will do the following:

• Find the volume of objects by considering the number of cubes that will fit into a space
• Find volume using standard and nonstandard unit measures
• Consider the increase in volume in solids when the scale factor changes (scaling up and down)
• Explore how volume formulas are derived and related

### Key Terms

Previously Introduced:

Volume: Volume is the three-dimensional space taken up by an object.

New in This Session:

Cone: A cone is a solid with a circular face at the bottom, a single point at the top, and a curved face connecting them.

Cross Section: A cross section is the face you get when you make one slice through a three-dimensional object.

Cylinder: A cylinder is a solid with two identical circles as faces at the top and bottom, and a single curved face connecting them. A cylinder can be considered a prism with an infinite number of edges!

Net: A net is a two-dimensional representation of a three-dimensional object.

Prism: A prism is a solid whose lateral edges are all parallel and which has two identical faces at the top and bottom. A prism can have any polygon as its base. Many tall buildings are prisms.

Sphere: A sphere is a solid made up of points all equidistant from a center in three dimensions. It is a perfect ball.

### Notes

Note 1

In this session, you will do the following:

• Find the volume of objects by considering the number of cubes that will fit into a space
• Find volume using standard and nonstandard unit measures
• Consider the increase in volume in solids when the scale factor changes (scaling up and down)
• Explore how volume formulas are derived and related

Note 2

Materials Needed:

• Transparent tape (optional)
• See-through graduated prisms (or cylinders). They can be purchased from ETA/Cuisenaire. (optional)
• Large, plastic 3-D models that can be filled with water, sand, or rice (rectangular prisms, triangular prisms, cubes, cones, pyramids, cylinders, spheres. Some need to be the same height and have the same radius or base.) They can be purchase from ETA/Cuisenaire (Power Solids). (optional)
• Modeling dough (optional)
• 6 cm to 9 cm strips of transparency film (optional)
• Rice (optional)
• Multilink cubes: Cubic units that can be connected together (cubic centimeters and 3/4 cubic inches). These can be purchased from:

Delta Education
80 Northwest Boulevard
P.O. Box 3000
Nashua, NH 03061-3000
Phone: 1-800-442-5444
http://www.delta-education.com

or:

ETA/Cuisenaire
500 Greenview Court
Vernon Hills, IL 60061
Phone: 800-445-5985/800-816-5050 (Customer service)
Fax: 800-875-9643/847-816-5066
http://www.etacuisenaire.com