An iceberg has a volume of 7655 cubic feet. What is the mass of the ice (in kg) composing the iceberg?
Hey guys, in this question they tell us that an iceberg has a volume that is 7655 cubic feet and what we need to do is we need to figure out its mass in kilograms, now to be able to solve this we need to know what the density of the iceberg is, now they don't give it to us within the question so we have to look for it, here when we find the density we see that the density of the ice berg equals 0.917 grams per centimeters cubed so we need to find kilograms which means we need to isolate grams so we need to isolate these grams here and how do we isolate those grams? We isolate those grams by canceling out the centimeters cubed on the bottom so we're going to start out with the feet cubed and with the feet cubed we'll change them into centimeters cubed and in that way isolate grams which we can then change to kilograms, alright so let's take a look here so we're going to say now we have 7655 feet cubed, now we're going to first change feet into inches, remember that 1 foot is equal to 12 inches but remember we can't cancel out feet cubed which is feet so we're going to have to cube this whole thing.
Now that we have inches cubed we can change those inches cubed into centimeters cubed so we put inches on the bottom, centimeters on top 1 inch is equal to 2.54 centimeters, we cube this entire thing as well so inches cubed can cancel out, now we have centimeters cubed and centimeters cubed we'll place here on the bottom, grams here on the top we're told that the density is 0.917 grams per 1 centimeters cubed so this cancels out with this, now we have grams, have to cancel out grams put grams on the bottom kilograms on top, 1 kilo is equal to 10^3 when we work this out it gives me 1.988x10^5 kilograms, our answer here has 4 significant figures because the number given to us initially has 4 significant figures, this density wasn't given to us we had to look it up since it wasn't given to us directly in the question we don't use it for the number of significant figures. So, guys this is the method that we have to use so that units cancel out so we're left with kilograms at the end