Converting Liters to Cubic Inches Using Dimensional Analysis

[courtrigrad]

The piston displacement of a car engine is given as 1.80 liters (L). Using only the facts that 1.00L = 1000 cm^3 and 1.00 in. = 2.54 cm, express this volume in cubic inches. So 1.80 L \times (\frac{1000 cm^{3}}{1.00 L})(\frac{1.00 in}{2.54 cm}) [/itex]. Would I have to cube the last term to cancel out the units?<br /> <br /> Thanks

 

[G01]

Yes. Cube the whole last proportion- (1.00in./2.54cm)^3. Remember, Your looking for cubic inches as well. There your solving for only inches.

 

[PhysicsDude55]

Yup. Whenever you convert units to a power, both sides of the convertion must be to the same power.

The answer should end up being aroung 16.8 IIRC, converting CC to cu. in. (I'm a car fanatic, and do these calculations often when figuring muscle car engines)