Why is the coefficient of volume expansion three times the coefficient of linear expansion?
348717
It actually is not, we just assume it because the difference is neglegible.If you want the exact relationship then go to google and search for thermal expansion.\nThose who say that it is 3 times are fools and dont know anything about physics.
208438
There is a delightful article by the late Dr. John Kenny on that, back a few years ago, looking at the formulae for surface area and volumes of spheres; I'll see if I can find it for you--it's in my files SOMEWHERE--and give you the reference, and the formulae he generated. It turns out that they're not precisely the same as what you've got--but not terribly far from it.\n\nAs I said, I'll see if I can find it, and I'll get you the reference and the formulae.\n\nAbout 9pm CST...\n\nOK, here is the formulae, done the best I can on this thing...\n\n\nFor a sphere of dimension 2*k, radius R\n\nVolume: (pi^k)*(R^(2*k))/k!\n\nFor a sphere of dimension 2*k + 1 and radius R\n\nVolume:\n(2^(2*k+1))*k!*(pi^k)* (R^(2*k+1))/(2*k+1)!\n\n\nTo get the surface areas for each of these, all you do is differentiate with respect to R...\n\nAs I said, it was a little more complex than you thought--the surface areas come out a little bit differently for odd and even numbered dimensions.  I do not recall why, frankly.
911209
volume is measured in liters or cubic meters
267532
If you need its volume, the formula is one third times the area of the base times the height.
270216
in a 2d object or representation, it would be the area. In a 3 dimensional object it would be the volume.
1144840
mass divided by volume\nmeasured in kgm^-3
1172136
try this and learn more about volume\nhttp://en.wikipedia.org/wiki/Volume
947213
Hi. Your link is bad. Usually there is a pressure applied to one of the pistons and the other exerts a force based on area difference. Twice the area, twice the force. Your ratio is .3 to 1.3. Hope this helps.
955775
Type "linear coefficient of thermal expansion" and "volume coefficient of thermal expansion" into you search engine.\nFor spheres, you probably want to use volume.\n\nYou should find formulas that relate change in length (or volume) and deltaTemperature.\n\nPlug the two temperatures and the coefficient into the formula and you will have the change in size.
814455
0 with 4 faces, 24 with 3 faces, 60 with 2 faces, 48 with 1 face and 12 with 0 faces.  \nNote, this is if the 3 cubes were not touching each other.  I made an assumption when you said that they were originally 3 separate cubes.  I believe, after reading the second answer, that I made an incorrect assumption since you said "total volume".  If the 3 cubes were touching each other when painted, I am wrong.
950567
x^1=x+(coefficient of linear expansion called alpha)*xt\nx^1=New length\nx=Original length\nt=change in temperature\n{values are given in table form in Physics or Engineering books}
905373
if u are referring to expansion due to heating than the order of expansion of the substances from lowest to largest is solid, liquids, than gases. But a solid's expansion is extremely low, almost impossible to measure unless its a metal.
993423
Don't know exactly, but because milk is mostly water, milk should have  a coefficient of expansion pretty close to that of water.
820189
Because the volume, pressure, and temperature are all related by Boyles Law and the Ideal Gas Law.\n\npv=nRt\n\nPressure times Volume equals the Number of molecules times the Gas Constant time the temperature.
846910
No. They do not share the same dimensions.\n\nYou can multiply them though.
407730
Let's look at the general case. It turns out that for even dimensional spheres, the ratio of the 'surface area' to the 'volume' of the next lower dimensional sphere is irrational in even dimensions and rational in odd dimensions. Your cases are just special cases of this general result.
63381
Conjecture A\nIf B is the area of the base pf a right rectangular prism and H is the height of the solid, then the formula for the volume is V= _?_\nConjecture B \nIf B is the area of the base of a right prism (or cylinder) and H is the height of the solid, then the formula for the volume is V= _? _\nConjecture C\nThe volume of an oblique prism (or cylinder) is the same as the column of the right prism (or cylinder) that has the same _? _ and the same _? _\nPrism-Cylinder Volume Conjecture\nThe volume of a prism or a cylinder is the _? _ multiplied by the _? _\nPyramid-Cone Volume Conjecture\nIf B is the area of the base of a pyramid or a cone and H is the height of the solid, then the formula for the volume is V= _? _ \nSphere Volume Conjecture\nThe volume of a sphere with radius r is given by the formula _?_\nSphere Surface Area Conjecture\nThe surface area, S, of a sphere with radius r is given by the formula _? _\n\nSolution 47916\n\n#1\nV = BH\n#2\nV = BH\n#3\nsame base area and same height\n#4 \nthe base area multiplies the height\n#5\nV = (1/3)BH\n#6\nV = (4/3)(pi)(r^3)\n#7\nS = 4(pi)(r^2)