Earth's diameter is approx 4 x the moon's. What is the ratio of their volumes?

Question

This is for a college class assignment that is due on Tuesday (12/4). What I have worked out so far is this:
Volume = 4/3 pi r^3; If the moon's diameter is n, then it's r = 1/2 n. Since the earth is 4 x this, then the earth's r = 2n.......right?

I'm getting for the moon: V= 4/3 pi (1/2n)^3
For the earth: V= 4/3 pi (2n)^3

How do you figure ratio.....if I've even done this much right?

Answer 1

Moon radius = r
Earth radius = 4r

V(moon) = (4/3) π r ³
V(earth) = (4/3) π (4r)³ = (4/3) π (64) r³

V(earth) : V(moon) = 64 : 1

Answer 2

It's been a long time. ...and I don't usually help with homework, but what the heck.

I don't know if your formulas are right, so I'll assume you've looked them up. As for the ratio, you could do one of two things: to find the ratio of the earth to the moon, you'd take V(earth) over V(moon). The 4/3 and pi would cancel, leaving (2n)^3 / (1/2n)^3 = then reduce to 8n^3 / 1/8n^3 = reduce to 8 / 1/8 = then 64:1.
Or, substitute a simple value for n, such as 1. If n = 1, then the answer becomes obvious. The formula is blahblahblah (8) / blahblahblah (1/8). See?

Or you can solve it logically - if the volume is solved using ^3, of the radius, and the ratio of the radii is 4:1, then the volume ratio must be 4^3:1^3, or 64:1.

Sometimes you gotta take a step back look at the big picture...

Answer 3

The Earth in those images IS 4 circumstances the dimensions of the lunar view from earth. human beings notoriously overestimate the straightforward length of the moon even as they recollect it from memory. If I were to inform you that the moon's length is in basic terms 0.5 the width of your pinkie finger even as held at arm's length, you probable don't have self belief it. yet attempt the evaluation the subsequent time you spot the moon, and also you'll see this is genuine. The evidence of the pudding might want to be to take a photo of the moon (without zoom). you'd be shocked how small it looks contained in the perfect image. about a million/4 of the dimensions of the earth in those Apollo images.

Answer 4

If the diam of the earth were 4 times the diameter of the moon, then the radius of the earth would be 4 times the radius of the moon.

Just take 4 and cube it. That will give it to you.

4 x 4 x 4 = 64 Ok?

Answer 5

plug some numbers in the original formula I plugged in a diameter of 12 and 48 for a R of 6 and 24 and work both formulas. I came up with 64 to 1.

Answer 6

V ol of a sphere = {4πr³/3}

If radius of moon is 'r' Moon then radius of Earth is '8r'

Ratio of Diameters is 8:1
Ratio of Vols is 8³ : 1
= 512 :1