Posted by Christy Williams on April 21st, 2016

Adult learners should be familiar with many mathematical conceptsand formulas. Among the most common is volume. Volume is defined as the amount of space occupied by a substance or object. It describes the capacity of a container or space. Volume is measured in square, or cubic, units.

### Formulas

Three-dimensional (3-D) figures each have length, width and height. These measurements are used in formulas to determine volume. Each 3-D shape has its own formula. The formulas for finding the volume (V) of 3-D figures are:

**Cone**

V = h/3 · π · r2, where *r* is the radius and *h* is the height.

**Cube**

V = *a*3, where *a* is the side of the cube.

**Cylinder**

V = π · r2 · h, where *r* is the radius and *h *is the height

**Pyramid**

V = 1/3 · b · h, where *b* is the base and *h* is the height.

**Rectangular Prism**

V = *l* · *w* · *h*, where *l* is the length, *w* is the width, and *h* is the height.

**Sphere**

V = 4/3 · π · r3, where *r* is the radius.

### Classroom Activities

As you teach the formula for volume, there are a number of classroom activities to demonstrate the concept and allow the students practice utilizing the formula in real life situations and for problem solving. Some activities include:

#### Around the House

Have students bring various items from around their homes (cups, storage containers, boxes, etc). Provide cubic unit manipulative pieces and allow them to work in pairs to find the area of the various items.

#### Gumball Guess

A popular game is having people guess the approximate number of gumballs in a container. Use the same concept in your class requiring the students to use the formulas to aid their guesses.

#### Modeling Volume

The Modeling Volume activity allows students to prove the use of the formulas with mini cereal boxes, 1-cm cube units and rulers. Students will see that the area is possible to find without stuffing the cereal boxes full and counting.

**Online Learning Activities**

In addition to hands-on classroom activities, several online resources provide learning opportunities focused on volume. Online learning activities can be found using the following links:

- Online Math Learning features a selection of games geared towards surface area and volume.
- Khan Academy provides tutorial videos along with practice problems.
- Study Ladder provides interactive practice accompanied by a tutorial video and follow-up printable worksheet. Activities for cylinder volume are also available.
- Study Zone offers a page of simplified instruction with a link to practice problems.

Teaching volume is more than just learning formulas. It requires teaching how to properly use the formulas to discover the correct answer. With this in mind, the more practice a student has, the more successful he will be. By providing multiple opportunities in the classroom and additional practice for home, the students will become more confident in the use of the formulas.

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