# Homework Help: Mass density of a sphere

1. Aug 18, 2009

### snubbly

Air in a sphere has density "x" kg/m3

If radius is halved and air is compressed... does density double? ("2x" km/m3)

2. Aug 18, 2009

### kuruman

One thing at a time. Suppose only one of these happened. Say the radius is halved. Does the density increase or decrease and by what factor? Once you figure that out, compress the air some more and see what happens to the final density relative to the initial.

3. Aug 24, 2009

### snubbly

Radius halved - density would increase.

I don't know by what factor though...

I have the Q&A ... initial is 1.4 kg/m3 and once radius is halved, density is 11 kg/m3.

I have to show working and I just can't figure it out.

Multiplying 1.4 by 7.9 gives me the answer, but I don't understand.

4. Aug 24, 2009

### mg0stisha

What's the magical 7.9? Or did you just do 11 kg/m3 / 1.4kg/m3

5. Aug 24, 2009

### snubbly

yes, just the 11 / 1.4.

clueless.

6. Aug 24, 2009

### mg0stisha

What all are you given in the problem?

7. Aug 24, 2009

### snubbly

This is the question from the textbook:

8. Aug 24, 2009

### mg0stisha

What happens to the volume of a sphere if the radius is halved?

9. Aug 24, 2009

### darkmagic

let say: D = Density
m = mass
v = volume

D1 = 1.4 kg/m3

mass is constant since the air will only be compressed.

D = m/v yielding m = Dv

Therefore, D1v1=D2v2

but v of sphere is (3*pi*r3)/4

and r2=r1/2

You can get it now.

Last edited: Aug 24, 2009
10. Aug 24, 2009

### mg0stisha

Minor correction: volume of a sphere is $$V = \frac{4\pi r^{3}}{3}$$

11. Aug 24, 2009

### darkmagic

Sorry. I interchanged 3 and 4.

12. Aug 24, 2009

### mg0stisha

got your back ;)

13. Aug 24, 2009

### darkmagic

Thanks.

14. Aug 24, 2009

### ideasrule

A intuitive way to think about this: Think about a cube. If you cut the side lengths in half, what happens to volume? Halve one dimension and volume halves. Halve the second and volume decreases by a factor of 4. Halve the third and volume goes down how many times?

The same thing happens to a sphere.

15. Aug 24, 2009

### snubbly

8.

Thank you, that really helped!

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