How many square centimeters are in 2.5 ft^2 ?

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Homework Help Overview

The problem involves converting an area measurement from square feet to square centimeters, specifically asking how many square centimeters are in 2.5 ft². The subject area pertains to unit conversion and dimensional analysis.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of dimensional analysis for unit conversion, noting the initial attempt to convert 2.5 ft² to centimeters without considering the squared units. There is a suggestion to apply the square correctly in the conversion process.

Discussion Status

The discussion has progressed with participants providing guidance on the correct application of dimensional analysis, particularly emphasizing the need to square the conversion factors. There appears to be a productive exchange of ideas, with participants acknowledging the clarification offered.

Contextual Notes

Participants are navigating the complexities of unit conversion, specifically addressing the distinction between linear and area measurements. The original poster expresses uncertainty regarding the conversion of square feet to square centimeters.

Beanie
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Homework Statement


How many square centimeters are in 2.5 ft^2 ?

Known:
1 inch≡2.54 cm
1 foot≡ 12 inches

Homework Equations

The Attempt at a Solution


2.5 ft^2/1 x 12in/1ft x 2.54cm/1in = 76.2 cm

I tried converting 2.5 ft^2 to centimeters by using dimensional analysis. However, I realized that it doesn't take into account that it is 2.5ft^2 not 2.5 ft. I don't know how to convert it to centimeters squared, rather than just cm.
 
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Beanie said:

Homework Statement


How many square centimeters are in 2.5 ft^2 ?

Known:
1 inch≡2.54 cm
1 foot≡ 12 inches

Homework Equations

The Attempt at a Solution


2.5 ft^2/1 x 12in/1ft x 2.54cm/1in = 76.2 cm

I tried converting 2.5 ft^2 to centimeters by using dimensional analysis. However, I realized that it doesn't take into account that it is 2.5ft^2 not 2.5 ft. I don't know how to convert it to centimeters squared, rather than just cm.

You are trying to use the correct technique (multiplying by different versions of "1" and cancelling units).

But use the squares correctly too... 1 = (12 in/1ft)^2 = 144in^2/1ft^2 and so on...

Does that help?
 
berkeman said:
You are trying to use the correct technique (multiplying by different versions of "1" and cancelling units).

But use the squares correctly too... 1 = (12 in/1ft)^2 = 144in^2/1ft^2 and so on...

Does that help?

Yes, thank you. This makes sense. So the correct answer is 2322.576 cm^2
 
Beanie said:
Yes, thank you. This makes sense. So the correct answer is 2322.576 cm^2

Yes, that looks correct. :smile:
 
berkeman said:
Yes, that looks correct. :smile:
Thank you!
 

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