How many square centimeters are in 2.5 ft^2 ?

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SUMMARY

The conversion of 2.5 square feet (ft²) to square centimeters (cm²) is accurately calculated as 2322.576 cm². The conversion process involves using dimensional analysis, specifically applying the relationships 1 foot = 12 inches and 1 inch = 2.54 cm. It is crucial to square the conversion factors when dealing with area measurements, leading to the equation: 2.5 ft² × (12 in/1 ft)² × (2.54 cm/1 in)² = 2322.576 cm².

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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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