- Solutions 16

(c) What is the engine piston displacement in liters of an engine whose displacement is listed as 450 in.^{3}?

Okay guys, so they tell us that the engine displacement is 450 cubic inches. They want to know what the displacement is in liters, so let's begin the conversion factors. So we have 450 cubic inches, we want to convert first inches to centimeters because then we could convert from centimeters to milliliters which means we could convert from milliliters to liters. So this is kind of the thought process that should be going on when you guys are figuring out how do I go from inches to liters so it's just connecting the different factors that you guys have learned before. So we know that for every one inch, you have 2.54 centimeters. Notice that the inches here is cubed which means we're going to have to cube the entire parenthesis and we know that one cubic centimeter equals one milliliter and then to go from milliliters to liters, we know that 1 milliliter equals 10 to the -3 liters.

So here we have 450 cubic inches, this one, remember if it's cubed it gets distributed to the number and to the unit so this becomes 16.387 cubic centimeters per cubic inches and then here we have the same thing. So now we're able to cancel out cubic inches with cubic inches, that's why we placed it on the bottom then centimeters cubed with centimeters cubed and then we can cancel out milliliters with milliliters. The fact that we have to cancel out units gives you a hint of where the placement of the values should be, whether you're multiplying or whether you're dividing. So after you cancel all of that out you're left with liters which is the unit that you're looking for. So when you multiply and divide everything your answer should be 7.32 liters. See you guys soon.