Can You Cover It?

Teacher Notes:

• Have students use different–sized cans for this activity. Then make a table on the chalkboard listing the area of the cover for each can and its volume (in grams or ounces). Have students enter their data into the table. Then have students use all the data in the table to make scatter plots of the surface area versus volume to see if there is a relationship.
• In Step 7, students may find the formula A = 2r(r + h) to be particularly useful in finding a solution.
• Have students make their own containers by constructing circles and rectangles that will form cylinders. Give them specific surface areas for the cylinders (use a value that is different from the one in Step 7) and compare the types of cylinders made using this set value. Students will need fairly stiff paper for this extension.

Procedure for the Activity

Answers:

Steps 1–3  See students’ work.

Step 4 

Step 5  A = 2r(r + h)

Step 6  See students’ work.

Step 7  Sample answer: r = 2 in. and h = 2 in.

Wrapping Up the Activity

See students’ work.