Question

The formula for the volume of a sphere is V = 4/3 ∏r3, where r is the radius of the sphere.
The radius of the Moon is 1/4 of the radius of the Earth. Answer the following questions.

a. If the volume of the Earth is V = 4/3 ∏r^3, write the volume of the Moon in terms of r.

b. Find the ratio of the volume of the Earth to the volume of the Moon.

Can someone help me with this question?

Answer 1

The radius of the Moon is 1/4 of the radius of the Earth
If the volume of the Earth is V = 4/3 ∏r^3 then r is the radius of the Earth.
So radius of the moon is 1/4 r
Plug that in the formula to get the volume of the moon.

Answer 2

Ok let me do that

Answer 3

1.45?

Answer 4

You can't possibly get a value by plugging (1/4 r) into the formula.
You should get a volume in terms of r.
Here's a start : \[V=\frac{ 4 }{ 3 }\pi r^3=\frac{ 4 }{ 3 }\pi (\frac{1}{4} r)^3\] Then simplify.

Answer 5

ok

Answer 6

so then it would be v= 0.07r^3?

Answer 7

It's better if you keep it in fraction form.

Answer 8

ok

Answer 9

To find the ratio Earth:Moon you put \[\frac{volume of earth}{volume of moon}\]

Answer 10

I got 64.71

Answer 11

For ratio ?

Answer 12

4.53:0.07
Is the ratio

Answer 13

I'm really confused

Answer 14

What's 64.71 for ?

Answer 15

I divided 4.53 by 0.07 for some reason. Its probably irrelevant.

Answer 16

OK, let's get back to where we were.
What did you get for the volume of the moon in fraction form

Answer 17

4/3*\[\pi\]1/64 r^3

Answer 18

It doesn't show very well for me, can you rewrite ?

Answer 19

yea

Answer 20

4/3 * pi* 1/64r^3

Answer 21

oh thanks water

Answer 22

np

Answer 23

Yes but still needs simplification (simplify 4 and 64)

Answer 24

1/48 *pi*r^3

Answer 25

I also got that

Answer 26

oh ok

Answer 27

Yep, correct !
Now for the last part
\[ratio=\frac{ volume~~of~~the~~earth }{ volume~~of~~the~~moon }\]

Answer 28

YAY

Answer 29

4/3*pi*r^3:1/48 *pi*r^3

Answer 30

then simplify it to be...

Answer 31

64/1

Answer 32

Yes ! 64:1 is the ratio !

Answer 33

Sorry for taking so much of your time

Answer 34

Not.At.All !
It's a pleasure =)