Surface Area with Curved Edge

I had my Math 31 students determine the area of the face with the curved edge from the this box to the right.  My intention was for them to use calculus techniques to determine the area even though that was not necessary.  One of my students was clever enough to notice that two boxes could be put together to form a rectangle and that area would be calculated and divided by 2 to get the area of the curved face.  They decided they would do the calculus and use the half rectangle as a check.  Perfect.


After taking some measurements they decided to superimpose this image onto a coordinate plane and come up with an equation that could model the curved edge.  All groups decided on a sinusoidal model for the curve and came up with the appropriate parameters from their measurements.

Once their equation was finalized they integrated and came up with an area.  Most groups did an "error analysis" with the "actual area" based on the rectangle made from two boxes placed together at their tops.
Some photos of student work can be found here and here and here.  The last two pictures are from the same group.


If you're reading this blog you will notice that I don't have a lot of blog entries.  Hence I'm not too sure what I should include or what else people might want to know.  I enjoyed this activity because the students had to do everything.  They had to decide on a function and determine appropriate parameters to make the curve fit the situation.  Some used cosine and some sine.  I guess one of the beauties of sinusoidal is the groups didn't all come up with the same equation.  Differences were based not only on measurements but where they put their origin. I liked that they had to retrieve the knowledge related to the parameters a, b and d for sinusoidal curves of the form y=asin(bx)+d or y=acos(bx)+d.

Any questions?  Feedback?  Suggestions?