Can You Cover It?

Materials: calculator, string, ruler, cylindrical food can, construction paper, sharp pencil

Work in pairs.

In this activity, you will make a paper covering for a food can. Then you will use the Distributive Property to help you find the amount of paper used for the can's "jacket."

Procedure for the Activity

Step 1 Get a cylindrical food can. Carefully trace around the bottom and top of the can onto a sheet of construction paper. Use a ruler to estimate the diameter of the circles, record the measurements, and then cut out the circles.
Step 2 Wrap a string around the can and cut it carefully so that the ends meet with no overlap. Measure and record the length of the string. Measure the height of the can and record this measurement. Make a rectangle to cover the sides of the can. Use the measurements you recorded for the distance and the height of the can. Check the fit of the cover for the can.
Step 3 Find the area of the paper you used to cover the can by using the information given below that you may recall from other mathematics courses that you have taken.
Fact 1: The area of a circle can be found by squaring the length of the radius and multiplying that sum by , which is about 3.14. A formula for the area is A = r² or A = 3.14r².
Fact 2: The distance around a circle is called the circumference. The circumference can be found by multiplying the length of the radius by 2 and then by . A formula for the circumference is C = 2r or C = 2(3.14)r.
Fact 3: The area of a rectangle is the product of the length and width or A = lw.
Step 4 Write a single formula for the total area of the paper used to cover the can. Combine the formulas in Step 3 such that total area = area of two circles + area of one rectangle. Use A for area, r for radius, and h for height of the cylinder.
Step 5 Use the Distributive Property to rewrite your formula from Step 4. The formula should begin like this: A = 2r( + ). Verify this formula by finding the area of the paper you used to cover the can. Compare the area you found in Step 3 with the area you found using this new formula.
Step 6 Explain which method you prefer for finding the amount of paper for covering the can you chose.
Step 7 Suppose the cover for a can has an area of 50 square inches. Find one possible set of dimensions for the can.

Wrapping Up the Activity

Make a poster or other display showing your work for this activity. Be creative. Consider decorating the cover you made for the can. Be sure to show how you found the area of the paper used for the can cover.