Understanding the Difference Between Square Inches and Inches Squared

  • Context: High School 
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SUMMARY

The discussion clarifies that '15 square inches' and '15 inches squared' are equivalent terms representing the same area measurement. It confirms that 1 square inch equals 1 inch squared, and similarly, 1 cubic foot is indeed the same as 1 foot cubed. The conversation also highlights that while 2 cubic feet equals 2 feet cubed, the dimensions of the cube differ; a cube measuring 2 cubic feet has a side length of approximately 1.27 feet, whereas a cube measuring 2 feet cubed has a side length of 2 feet. The calculations presented demonstrate that a box measuring 2.15 feet on each side has a volume of 9.94 cubic feet, which translates to approximately 72.5 gallons.

PREREQUISITES
  • Understanding of basic geometry concepts such as area and volume
  • Familiarity with units of measurement, specifically square and cubic units
  • Basic mathematical skills for calculating area and volume
  • Knowledge of conversion between cubic feet and gallons
NEXT STEPS
  • Research the mathematical principles of area and volume calculations
  • Learn about unit conversions between cubic feet and gallons
  • Explore practical applications of square and cubic measurements in real-world scenarios
  • Investigate common misconceptions regarding dimensional measurements in geometry
USEFUL FOR

Students, educators, and professionals in fields requiring precise measurements, such as engineering, architecture, and chemistry, will benefit from this discussion.

Agahnim
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What's the difference between '15 square inches' and '15 inches squared'. I always thought there was a difference but now am being told that both are the same. If that's the case...

Then how does 1 sq. inch = 1 in squared?

Also...

Is 1 cubic foot the same as 1 foot cubed? Yes, that would seem to be the case.

However...does this hold for other numbers as well? Do 2 cubic feet = 2 ft. cubed? Or is it that 2 cubic feet would be a cube that is 1.27 ft on each side, while 2 ft. cubed would be a cube that measures 2 ft. on each side?
 
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15 inches squared is 225 square inches.
 
"15 inches squared is 225 square inches."

Hi,
I think if the AREA is 15 in. squared, that is the same as 15 square inches. This is the only way any of this makes sense to me.

Therefore...if area is given as 15 in ^ 2, that is the same as 15 square inches.
 
Perhaps I ought to have said 15 inches square and not squared
 
Hi,
Its ok, I am pretty confused about this thing as it is and no doubt confusing others in the process too!

Basically...I was doing a chem. problem and my calculations showed that a 2.15 X 2.15 X 2.15 foot box (just very little bigger than 2 feet on each side) would take 75 gallons to fill! I couldn't believe it and that's how this whole thing started. (One only needs to take a ruler and measure it against the walls to see how small this box would be, like I just did...He'll be surprised I am sure!)

But my calculations are right...it would take 75 milk jugs from one's fridge right now to fill a small box like that!

Sheesh...crazy!
 
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One gallon is 0.137 cubic feet- not very large. A cube 2.15 feet on a side ("2.15 feet square") has volume 2.15x2.15x2.15= 9.94 cubic feet or 9.94/0.137= 72.5 gallons.
 

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