In this exploration you will work with your team (table) to take some measurements of a cylinder to discover the formula of a surface area on your own.
Objective:
At the end of this lesson you should be able to calculate the surface area of all cylinders.
Directions:
Task 1: After being given your cylinder to work with for the day. You will need to make sure everyone has a sheet of paper to take down the measurements you will be asked to record. In addition, you will want to take pictures to throw into a Keynote.
Task 2: After everyone has taken out a sheet of paper and a pencil, measure the following pieces:
a) height of the cylinder in cm = ______
b) diameter of the cylinder in cm = ______
c) radius of the cylinder in cm =_______
d) circumference of the cylinder in cm =_______
Task 3: Now calculate the following pieces:
a) circumference of the cylinder in cm =_______
b) area of the triangle in cm =_______
Task 4: With your group and without a formula make a conjecture as to what the lateral surface area will be of the cylinder
Task 5: After you have completed Tasks 1-4 please show your teacher immediately before you move on.
Task 6: After your teacher has checked off the checklist for Tasks 1-4, select a partner table to work with only to share the cylinder.
Task 7: After you have selected your partner table you will need to make one cut at the halfway point of the cylinders, and cut again at the base of the cylinder so that it can be spread across a net. After you have two equal pieces of the cylinder, split one piece with your partner group and continue to work only in your partner groups.
Task 8: Calculate the surface area by hand taking into account what the actual height should be. Does it match your conjecture that you made in Task 5?
Debrief Questions:
1) Does your conjecture for the lateral area match the one you calculated?
2) How can you simplify the the steps for finding the lateral surface area of a cylinder.
3) Find the surface area of the triangle.
4) What can you summarize about each choice above.
Task 9: Compile a Keynote to summarize what you have learned