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The diameter of the Moon is 3480 $\mathrm{km}$ . What is the volume of the Moon? How many Moons would be needed to create a volume equal to that of Earth?

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Physics 101 Mechanics

Chapter 1

Introduction, Measurement, Estimating

Physics Basics

Loki M.

May 28, 2021

What power is needed to move a 13.4 kN car up an 8 degree incline with a constant speed of 80 kph against a frictional force of 360 N?

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Hope College

University of Sheffield

Lectures

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

09:56

In mathematics, algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.

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The diameter of the Moon i…

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(III) The diameter of the …

The mean radius of the Ear…

Our question says that the diameter of the moon is 3,480 kilometres. What is the volume of the moon and how many moons would be needed to create a volume equal to that of the earth? Okay, so I wouldn't hand wrote down what we have given here we have the diameter of the moon, which I write as disobey M is equal to 3,480 kilometers. We also know that the radius of the earth, which you could look up on liner is written in the textbook is 6.38 times 10 to the six meters. So the radius of the moon then is also given because the radius of the moon is just that equal to the diameter of the moon divided by two which is 1,740 kilometers or 1,740 times 10 to the third meters. That's because, and I'll write the south for visual aid. One kilometer is equal to one times 10 to the third meters. So that's how I did that conversion to get our radius of the moon written and meters. So then the question is first, what's the volume of the moon? And then how many of those moons would you need to make up the volume of the Earth? Essentially, what's the ratio of the volume of the moon to the volume of the Earth? So first, let's find the volume of the moon going with the men is going to just be equal to the volume of the sphere where the radius is that of the moon. So 4/3 pi r to the third. Where are here is the radius of the moon. So 4/3 pi times the radius of the moon to the third. So if you plug in 1,740 times 10 to the third as your radius of the moon, this comes out to give you a volume of 2.21 times 10 to the 19 cubic meters. Okay? No, it's a little more like three. There we go. The box that in his air volume of the moon. Okay, so next thing it wants to know, because it wants us to find how many moons we would need to create a volume equal to that of the Earth. So essentially it wants us to find the ratio of the volume of the moon to the volume of the earth. So go ahead and find this ratio. Buy me the moon volume on earth again approximating both of them to the spheres. You have 4/3 pi times the radius of the moon cute, divided by 4/3. Hi. Okay. Times the radius of the earth. Cute. Well, the 4/3 pi cancelling both instances, right? And so we're going to be left with the radius of the moon divided by the radius of the earth cubed. So we'll plug in our radius of the moon, which is 1,740 times 10 to the third meters. Right. And we'll divide that by our radius of the earth, which was 6.38 times 10 to the six meters. And we will cube all of that. And that gives us 49.3. So we'll box it in as their solution to how many moons you could fit the volume of the Earth

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