Titania, the largest moon of the planet Uranus, has 1/8 the radius of the earth and 1/1700 the mass of the earth. (b) What is the average density of Titania? (This is less than the density of rock, which is one piece of evidence that Titania is made primarily of ice.)

Video transcript

Welcome back everybody. We are told that the radius of Jupiter is about 11.2 times that of the radius of Earth. We are also told that the mass of Jupiter is 317 times the mass of Earth. Now we need to determine what the density of jupiter is given, that the density of earth is 5500 kg per meter cubed. And just as one more assumption here we are told that jupiter is a sphere, which makes our calculations fairly easy. So here's what we're gonna do. We're gonna start out with the formula for the density of jupiter and try to eventually sub in this value right here. So the density of jupiter is just going to be the mass of jupiter divided by the volume of jupiter. Well, we know that the mass of jupiter is times the mass of earth. I'm just going to expand the bottom here. The volume of jupiter is going to be four thirds times pi times the radius of jupiter squared. Well, we know what the radius of jupiter is equal to this bottom part is now going to be four thirds pi times 11.2 times the radius of earth cubed. Now, I'm gonna take out some of the constants and numbers to the front here, we're gonna have 317 divided by 11.2 cubed times the mass of earth over four thirds pi times the radius of earth cubed a K. A the volume of earth, which this term right here just simplifies down to the density of earth, which we are given. So let's go ahead and plug in that value here, we have found our constant or a factor right up front. We just need to plug in the density of earth, which is 5500 kg per meter cubed, giving us that the density of jupiter is kg per meter cubed. Giving us a final answer choice of B. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.