 Okay, let's continue our density discussion by doing this type of a problem, the density of a sphere. So it says a star is estimated to have a mass of 2 times 10 to the 36 kilograms. Assuming it to be a sphere of average radius of 7.6 times 10 to the 5th kilometers, calculate the average density of a star in units of grams per cubic centimeter. Okay, and I have all of the information that you were given from the problem, the mass of the star, the radius of the star, and the density of the star. Now remember, and you need, you want to solve the density for the density of the star. Now remember for the density, we need to know mass per unit volume. So in other words, we need to figure out what the volume is of a sphere and how it actually relates to the radius. So if you recall from geometry class, volume equals 4 thirds pi r cubed. So r being the radius, right, so from this we should be able to figure out the volume of the star. So 4 thirds times pi times the radius of 7.6 times 10 to the 5th kilometers cubed. So let's solve for that, pi times 4 divided by 3, okay, and if hopefully you get the same number as I do, to two significant figures, right, so it's going to be 1.8 times 10 to the 18th kilometers, okay, cubed. So when we look here, we want centimeters cubed, that's not kilometers cubed. So we're going to have to, what do you say, convert from kilometers cubed to centimeters cubed. Also when we look over here, we've got kilograms for the mass of the star, but we want grams for the density. So let's remind ourselves how to change kilograms to grams, so one kilogram for every 1000 grams, so kilograms cancel, and that's one to the third plus 36, so it's going to be 2 times 10 to the 39 grams. That's the mass of the star, okay, pretty massive. So remember here, right, for every kilometer, we've got to figure out, well, what's the conversion, one kilometer, how many centimeters do we have for each kilometer? So remember, a kilometer is one to the third meters, and a meter is one to the second centimeter, so if you add those two up, every kilometer is one times 10 to the fifth centimeters, but we have cubed here, so we can multiply the times 10 to the fifth centimeters per kilometer three times, or we could just do like this. So hopefully, you see, kilometers cubed, it's canceled, but we've got to cube one to the fifth centimeters, or one times 10 to the fifth centimeters. When we do that, of course, it's five plus five plus five, which is 15, alright, so it's 1.8 times 10 to the 18th, one times 10 to the 15th centimeters, okay? So, now let's multiply those two numbers together, so the times 1, E, 15, that way you get 1.8 times 10 to the 33rd centimeters cubed, because that's all the units we've got left. Okay, so we've got grams, we've got centimeters cubed, so let's figure out the density. Okay, density is grams per centimeters cubed, so 2 times 10 to the 39th grams divided by 1.8 times 10 to the 33th centimeters cubed. So hopefully, everybody sees, we have the right units there, grams per centimeters cubed, and now we just plug and check. So, 2, E, F, and we get... So, this is two sig figs, this is one sig fig, so there's only one sig fig, so one times 10 to the 1, 2, 3, 4, 5, 6, 6 grams per cubic centimeter. So that's the density of this particular star to the right number of sig figs. Okay, so hopefully there aren't any questions. If there are, feel free to email me about it, okay? Thank you.