Area and Volume Units
and Dimensional Analysis

Follow the instructions below to make a series of measurements and calculations. You may work with a partner but everyone must write down the measurements and perform the calculations on their own paper. Use a ruler and meterstick/yardstick to make your measurements.

Part 1: Area

1. Measure the length and width of a book cover in cm to the nearest 0.01 cm. Calculate the area in cm². Write your measurements and calculations here.
2. Measure the same book’s length and width in inches to the nearest 1/16 of an inch. Calculate the area in in². Write your measurements and calculations here.
3. Write your result from measurements for the area of the book cover in cm². Convert it to in², showing your work for the calculation.
4. Write your result from measurements for the area of the book cover in in². Convert it to cm², showing your work for the calculation.
5. Evaluate your results by comparing the area values from measurement to the values you obtained by converting from one unit to another.
   1. Why are they not exactly the same?
   2. Are they close enough to each other to prove that the conversion math is accurate?

Part 2: Volume

1. Measure the length, width, and height of a fish tank in m to the nearest 0.0001 m (1/100 of a cm). Calculate the volume in m³. Write your measurements and calculations here.
2. Measure the same tank’s using feet to the nearest 1/16 of an inch. You will have to convert feet and inches and fractions of an inch to decimal feet. Calculate the volume in ft³. Write your measurements and calculations here.
3. Write your result from measurements for the volume of the fish tank in m³. Convert it to ft³, showing your work for the calculation.
4. Write your result from measurements for the volume of the fish tank in ft³. Convert it to m³, showing your work for the calculation.
5. Evaluate your results by comparing the volume values from measurement to the values you obtained by converting from one unit to another.
   1. Why are they not exactly the same?
   2. Are they close enough to each other to prove that the conversion math is accurate?

Part 3: Speed

1. Measure the length of the room in feet or meters and write it here.
2. Assume you walk at 2 mi/hr. Calculate the number of seconds it would take at this speed to walk the length of the room. Show work for your calculations here.
3. Try it. Time yourself walking the length of the room. Write down your result here.
4. Was your result close to your calculation? Why was it not exactly the same?