Lesson 6: Surface Area and Volume Problem Solving
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How does adjusting the dimensions of a 3-D object affect its surface area and volume? In the following Math Lab, you will investigate this question.
Math Lab: Surface Area and Volume Analysis
Go to Math Lab: Surface Area and Volume Analysis, print it (or copy by hand) and complete it. Save your work in your course folder (binder).
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Take a look at the results from Math Lab: Surface Area and Volume Analysis.
It seems reasonable to assume that as the dimensions of an object are doubled, the surface area and volume are also doubled. Yet the results of the investigation proved otherwise.
In fact, you may have found that as the dimensions are doubled, the surface area is quadrupled, or increases by a factor of four.
At the same time, the volume undergoes an increase by a factor of eight! Where do these numbers come from?
Review your lab results and see if you can see any patterns in the ratios.
You may want to extend the investigation by quadrupling each dimension; then recalculate the surface area or volume.
Develop an explanation for how to predict the increase in surface area or volume.
Use your explanation to predict how the surface area and volume will change when the dimensions of an object are increased by a factor of 7.
If possible, work with other students to see if you can develop a formula or pattern for the change in surface area and volume.
To check your work, use the link below.