Question

How many gallons are in 1.00 cubic feet? use dimensional analysis.

Answer 1

What unit conversion factors do you have available?

Answer 2

\[1cm ^{3}=1 ml\]
2.54 cm = 1 in
1.06 l = 1 qt
and all the other normal conversion rates...

Answer 3

Ok, then I think the path will be from feet to inches to centimeters to milliliters to liters to quarts to gallons.

Answer 4

how would you convert cm3 to in?

Answer 5

would you have to cube 2.54?

Answer 6

Yes, and the 12 inches per foot.
\[1.00ft^3 \cdot \frac{12^3inch^3}{ft^3} \cdot \frac{2.54^3cm^3}{inch^3} \cdot \frac{1ml}{1cm^3} \cdot \frac{1liter}{1000ml} \cdot \frac{1quart}{1.06liters} \cdot \frac{1gal.}{4quarts}\]

Answer 7

All the units cancel except for gallons, so multiply and divide as needed and round to 3 sig.figs.

Answer 8

okay. thanks...lemme calculate it and ill tell you if it works out :)

Answer 9

i got 6.68...sounds okay, right

Answer 10

Sounds reasonable.

Answer 11

Ok, I checked it on my calculator and got the same.
Do you understand how the process works now? It's all a matter of arranging the conversion factors so that the units you don't want cancel out, and the unit you're changing to is left in the numerator.