Topics
7. Geometry
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United States of America
Grade 7

Investigation: Formula for surface area of cylinders

Lesson
Practice
Overview
Activity
Reflection

Investigate how to find the surface area of a cylinder.

Objectives
  • To recognize the shapes that make up the net of a cylinder.
  • To calculate the surface area of a cylinder.
Materials
  • Cardboard toilet paper rolls or paper towel rolls
  • Paper
  • Tape
  • Scissors

Finding the surface area of a cylinder

We're going to develop the formula for surface area of a cylinder
Notice the shape of the ends of the cardboard roll. Using your paper and scissors, create two ends that could be taped onto the ends of the roll to make a complete cylinder. What shapes did you cut out to make a complete cylinder? Find the area of these shapes.
Now cut the cylinder in a straight line and unroll the cardboard so it can be placed on a table. What shape is created by the unrolled cardboard? Find the area of this shape.
Investigate
Consider the following questions once you have completed the above procedure.
1.
What shapes make up the net of a cylinder?
2.
What is the total surface area of your cylinder?

Answer the questions below after you have completed the activity.

Discussion
1.
What is the relationship between the length of the curved surface of the cylinder and the circumference of the top and bottom shapes?
2.
Using the area formulas for the shapes that make up the net of a cylinder, create a formula for the surface area of a cylinder.

Outcomes

7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

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