How do I convert 35.2 ft^2 to cm^2 using dimensional analysis? ie, what are the steps when you have units squared?
To convert 35.2 ft^2 to cm^2 using dimensional analysis, you can follow these steps:
Step 1: Determine the conversion factor between square feet (ft^2) and square centimeters (cm^2).
- 1 ft = 30.48 cm (conversion factor for length)
- Convert to square units by squaring both sides: (1 ft)^2 = (30.48 cm)^2
- Simplify: 1 ft^2 = 929.0304 cm^2
Step 2: Set up the conversion factor as a fraction, placing the desired unit (cm^2) in the numerator and the given unit (ft^2) in the denominator.
- Conversion factor: 929.0304 cm^2 / 1 ft^2
Step 3: Multiply the given value (35.2 ft^2) by the conversion factor, canceling out the unwanted unit (ft^2) and keeping the desired unit (cm^2).
- Calculation: 35.2 ft^2 * (929.0304 cm^2 / 1 ft^2)
Step 4: Perform the calculation to find the final answer.
- 35.2 ft^2 * (929.0304 cm^2 / 1 ft^2) = 32,641.472 cm^2
Therefore, 35.2 ft^2 is equal to 32,641.472 cm^2.
1in = 2.54cm
so, 1in^2 = (2.54cm)^2 = 6.45cm^2
You know that you can always multiply by 1 without changing things. Dimensional analysis is just a way of multiplying by 1 that gets rid of the units you don't want, leaving behind the units you do want. It solves the problem of "what do I divide by?" or "do I multiply instead?"
You always multiply. By 1.
If 1in = 2.54cm, then divide by cm, and you get
1in/2.54cm = 1
similarly, 2.54cm/1in = 1
You want to convert from ft^2 to cm^2. I don't recall how many cm in a foot, but I do remember 2.54cm/in. So,
35.2ft^2 * (12in/ft)^2 * (2.54cm/in)^2 = (35.2*144*6.45)cm^2
You can check this at any of the many online unit conversion web sites.
The unwanted units cancel out, just as do common factors when reducing fractions to lowest terms. All we are left with is cm^2, as we wanted.