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# Sphere mass vs. surface area

## Sphere mass vs. surface area - Physics Forum

### Sphere mass vs. surface area - Physics Forum. Discuss and ask physics questions, kinematics and other physics problems.

#1
10-12-2007, 11:48 PM
 Ernie Sty Guest Posts: n/a
Sphere mass vs. surface area

If you have two spheres, one of them has a mass of 100 and a surface area of
100, and the other one has a surface area that is 70% less than the first
and has the same density, how much mass will the second sphere have?

I'm looking into this hypothesis (for fun ONLY) that when all the continents
were together, they made up the entire surface of the earth, and their
splitting and drifting apart was caused as the earth somehow expanded.
Please don't feel the need to debunk that theory, I'm taking it with a grain
of salt. I just want to figure out how much the earth has increased in mass
if that hypothesis is true and if the density has remained constant, but I
don't know how.

#2
10-13-2007, 12:21 AM
 OG Guest Posts: n/a
Sphere mass vs. surface area

"Ernie Sty" <[Only registered users see links. ]> wrote in message
news:[Only registered users see links. ] ...

Area of sphere = 4 * pi * R^2

Volume of sphere = 4/3 * pi * R^3

Calculate the radius for 2 cases, when the area is 1 and when the area is
0.3

Then calculate the volume for both cases..

Assume the same density for both, and calculate the mass for both cases.

#3
10-13-2007, 12:21 AM
 OG Guest Posts: n/a
Sphere mass vs. surface area

"Ernie Sty" <[Only registered users see links. ]> wrote in message
news:[Only registered users see links. ] ...

Area of sphere = 4 * pi * R^2

Volume of sphere = 4/3 * pi * R^3

Calculate the radius for 2 cases, when the area is 1 and when the area is
0.3

Then calculate the volume for both cases..

Assume the same density for both, and calculate the mass for both cases.

#4
10-13-2007, 12:29 AM
 N:dlzc D:aol T:com \(dlzc\) Guest Posts: n/a
Sphere mass vs. surface area

Dear Ernie Sty:

"Ernie Sty" <[Only registered users see links. ]> wrote in message
news:[Only registered users see links. ] ...

A1 = 100 = 4 * pi * r1^2 :. r1 = sqrt(25/pi)
V1 = 4/3 * pi * r1^3 = A1 * r1 / 3
A2 = 70 = 4 * pi * r2^2 :. r2 = sqrt(17.5/pi)
V2 = A2 * r2 / 3

M1 = V1 * rho1
M2 = V2 * rho2
rho1 = rho2
M1 / V1 = M2 / V2 :. M2 = M1 * V2 / V1

Solve for r1. Solve for V1. Solve for r1. Solve for V2. Solve
for M2.

*!* if the density has remained constant *!*

An assumption that whomever you are / will be arguing with will
jump through.

David A. Smith

#5
10-13-2007, 12:29 AM
 N:dlzc D:aol T:com \(dlzc\) Guest Posts: n/a
Sphere mass vs. surface area

Dear Ernie Sty:

"Ernie Sty" <[Only registered users see links. ]> wrote in message
news:[Only registered users see links. ] ...

A1 = 100 = 4 * pi * r1^2 :. r1 = sqrt(25/pi)
V1 = 4/3 * pi * r1^3 = A1 * r1 / 3
A2 = 70 = 4 * pi * r2^2 :. r2 = sqrt(17.5/pi)
V2 = A2 * r2 / 3

M1 = V1 * rho1
M2 = V2 * rho2
rho1 = rho2
M1 / V1 = M2 / V2 :. M2 = M1 * V2 / V1

Solve for r1. Solve for V1. Solve for r1. Solve for V2. Solve
for M2.

*!* if the density has remained constant *!*

An assumption that whomever you are / will be arguing with will
jump through.

David A. Smith

#6
10-15-2007, 04:32 PM
 Ernie Sty Guest Posts: n/a
Sphere mass vs. surface area

"N:dlzc D:aol T:com (dlzc)" <[Only registered users see links. ]> wrote in message
news:yjUPi.23\$[Only registered users see links. ]...

I appreciate your effort, but it's too high-level for me. Thanks though.

Like the assumption that I am or will be arguing with someone about it? ;-)
I'm not the slightest bit interested in arguing with anyone about the
expanding earth hypothesis (or theory, or whatever it is.) I know far too
little about the whole thing to argue intelligently about it. It sounds
very unlikely to me, but I just don't know.

All I want to know is approximately how much the mass of the earth has
increased if the expansion is true and the density remained constant.

#7
10-15-2007, 04:32 PM
 Ernie Sty Guest Posts: n/a
Sphere mass vs. surface area

"N:dlzc D:aol T:com (dlzc)" <[Only registered users see links. ]> wrote in message
news:yjUPi.23\$[Only registered users see links. ]...

I appreciate your effort, but it's too high-level for me. Thanks though.

Like the assumption that I am or will be arguing with someone about it? ;-)
I'm not the slightest bit interested in arguing with anyone about the
expanding earth hypothesis (or theory, or whatever it is.) I know far too
little about the whole thing to argue intelligently about it. It sounds
very unlikely to me, but I just don't know.

All I want to know is approximately how much the mass of the earth has
increased if the expansion is true and the density remained constant.

#8
10-15-2007, 05:13 PM
 dlzc Guest Posts: n/a
Sphere mass vs. surface area

On Oct 15, 9:32 am, "Ernie Sty" <[Only registered users see links. ]> wrote:

Correction:

r1 ~= 2.82
V1 ~= 94.0
r2 ~= 1.55
V2 ~= 15.5

It is the invert of the problem originally stated:
M1 / M2 = V1 / V2 = 94.0 / 15.5 = 6.06
The mass will have had to increase by about 6 times in the period of
consideration.

David A. Smith

#9
10-15-2007, 05:13 PM
 dlzc Guest Posts: n/a
Sphere mass vs. surface area

On Oct 15, 9:32 am, "Ernie Sty" <[Only registered users see links. ]> wrote:

Correction:

r1 ~= 2.82
V1 ~= 94.0
r2 ~= 1.55
V2 ~= 15.5

It is the invert of the problem originally stated:
M1 / M2 = V1 / V2 = 94.0 / 15.5 = 6.06
The mass will have had to increase by about 6 times in the period of
consideration.

David A. Smith

#10
10-15-2007, 10:44 PM
 PD Guest Posts: n/a
Sphere mass vs. surface area

On Oct 12, 6:48 pm, "Ernie Sty" <[Only registered users see links. ]> wrote:

(0.3)^(3/2) times the original mass. That's 0.3 to the power 3/2, or
if you like, the square root of 0.0027.

 Tags area , mass , sphere , surface

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