Question

Use the dimensional analysis to convert 13 in² to cm²

Answer 1

To convert 13 square inches to square centimeters using dimensional analysis, multiply 13 by the square of the conversion factor 2.54 cm per inch. The calculation is 13 * (2.54)^2, which gives an area of approximately 83.8708 cm².

Step-by-step explanation:

To convert 13 square inches (in²) to square centimeters (cm²) using dimensional analysis, we will use the conversion factor that 1 inch is equal to 2.54 centimeters. Here's the step-by-step explanation of the dimensional analysis method:

1. State the given quantity:
   13 in².
2. Write the conversion factor between inches and centimeters as a ratio:
   1 in = 2.54 cm.
3. Since we are dealing with square inches, we need to square the entire conversion factor to convert to square centimeters:
   (2.54 cm/1 in)².
4. Set up the conversion such that the unit you want to remove (in²) is opposite of the unit in your conversion factor, allowing them to cancel out:
   13 in² * (2.54 cm/1 in)².
5. Multiply the numbers and calculate:
   13 * (2.54 * 2.54) cm².
6. Complete the calculation:
   13 * 6.4516 cm².
7. The result is the converted measurement in square centimeters:
   13 * 6.4516 cm² = 83.8708 cm².

The area of 13 in² is thus equivalent to approximately 83.8708 cm² when using dimensional analysis for the unit conversion.