## Cylinder Surface Discovery

### Carol SpiceSanta Rosa District Schools

#### Description

Help your students understand the surface area of a cylinder with this simple lesson where students create their own cylinders.

#### Objectives

The student uses concrete or graphic models to create formulas for finding surface area of prisms and cylinders.

#### Materials

- Compasses and rulers - one per student is ideal
- Paper, pencil
- Tape or glue
- Examples of cylinders - soup can, ice cream bucket, etc.

#### Preparations

1. Gather at least three examples of cylinders; soup can, ice cream bucket, etc.
2. Assemble materials: Plain paper, compasses, and rulers.
3. Provide students with the formulas for circumference of a circle, area of a circle, and area of a rectangle.
4. Write the questions from the procedures on the board or overhead.

#### Procedures

1. Show students the example cylinders asking how they could find the surface area. Allow time for brainstorming and list ideas on the board.

2. Pass out paper, compasses and rulers. Review needed formulas and vocabulary such as circumference, radius, diameter, area, etc.

3. Give the students the following directions. (If the students will be using glue, you will have to instruct them to make tabs on the circles.) Model each step as you go over it.
1. Draw two circles each with a radius of 2 inches.
2. Carefully cut out the circles.
3. Make a rectangle with a side that will be able to wrap aroud the circle.
4. Show the students how to make a cylinder from the two circles and the rectangle. Have the students copy and answer the following information:

Circumference of the circle =

Find the area:
Area of circle 1 =
Area of circle 2 =
Area of the rectangle that makes the side of the cylinder =

Total surface area of your cylinder =

5. Use your model and show students how to find the surface area of the cylinder. Circulate and assist students in making the cylinders and answering the questions.

6. Discuss with students the following concepts:
- the parts of the cylinder that must be considered when finding surface area (two circles and a rectangle)
- how the circumference of the circle relates to the side of the rectangle
- how the height of the cylinder relates to the other side of the rectangle

7. Extend the discussion by asking if this might apply to finding the surface area of a cone.

8. Ask students to write a paragraph explaining what they just did to find the surface area of a cylinder.

#### Assessments

1. Informally assess students' understanding by looking at the model cylinders they have made.
2. Questions will be collected and assessed.
3. Paragraphs should be assessed and should include: the formulas, the steps for determining the shapes that make up a cylinder, and the steps to determine the surface area.