what does 4/3 part of the volume of a sphere mean?
600264
Two Hemisphere...may be
1087751
The amount of air is the difference in volumes.\nA = V(r+1) - V(r) = (4/3)pi (r+1)^3 - (4/3)pi r^3\nA = (4/3)pi((r+1)^3 - r^3)
574480
The volume of the whole sphere is V = (4/3)πr^3 = (4/3)π(1000) = 4000π/3.  The unfilled part is a spherical cap with a volume V = (π/6)(3a²+h²)h, where a is the radius of the base of the cap and h is its height.  So subtracting 14 from 20, h = 6.  Using Pythagoras, a² = 10²-4² = 84.  That makes the volume of the cap π*(3*84+36)*6/6 = 288π.  Subtracting cap from sphere leaves 4000π/3 - 864π/3 = 3136π/3 (exactly) = 3284.01 cubic meters (approximately).
418584
The rate of increase of the volume dV/dt can be solved as dV/dr*dr/dt (chain rule)\n\nYou are given that dr/dt = .04 cm/s and you can derive dV/dr from the volume formula.  The derivative of r^n is n*r^(n-1) so the derivative of r^3 is 3r^2.  The derivative of the volume formula is 4/3*pi*3r^2, or 4pi*r^2.  Therefore the sphere is growing at 4pi*r^2 in volume per radius length.\n\n(a)\nif r = 10cm then the rate of increase of volume, dV/dt = dV/dr * dr/dt = 4*pi*(10cm)^2*(.04cm/s)\nDo the math and you should get an answer in cm³/s\n\n(b)\nGiven V=36, find r.  The area of the cross section = pi*r².  The rate of increase of that area is 2*pi*r*dr/dt.\n\n(c)\nIf dV/dt and dr/dt are the same number then dV/dr=1.  Find r so that dV/dr=1.
885732
well...lets call your known volume V.  so...what kind of shape are we dealing with...eh, lets claim we are dealing with a sphere...we know the volume of the sphere is determined by v=(4/3)*pi*r^3 so we could solve for r (the radius).\n\nso....\n\nV=(4/3)*pi*r^3\nr=((3V)/(4pi))^(1/3)\n\nwe can now substitute that r into our surface area of a sphere equation....which is SA=4*pi*r^2, so we would have\n\nSA=4*pi*((3V)/(4pi))^(2/3)\n\na similar series of actions would occur for any other shape\n\nhope this helps,\n\nMatttlocke
760290
Popcorn ball. . . . \n\nGoogle search:  volume sphere (should have used "volume sphere," but it turned out not to matter)\n\nhttp://www.aaamath.com/geo79-volume-sphere.html\n\n4/3 (pi) r^3\n\n4/3 times pi times (6 to the 3rd power) \n\nequals 4/3 times pi times 216. . . and work from there.\n\nGoogle search:  volume cylinder\n\nhttp://www.321know.com/exp79_x5.htm\n\n(area of the base) * height =(pi r squared times height)\n\nPi times (16 squared) times 275. . . work from there.
342254
The volume V of the sphere is the sum of the volumes of all the "almost pyramids" with bases B1, B2, B3,........\n\nV = 1/3B1r + 1/3B2r + 1/3B3r + 1/3B4r + ........\nV = 1/3r( B1 +B2 + B3 + B4 + ......)\n\nThe sum of the bases is the surface area (S.A.) of the sphere. The volume V is 4/3¶3. Substituting,\n\n4/3¶r3 = 1/3r * S.A.\n\nTo solve for the surface area, multiply both sides by 3/r.\n\n3/r * 4/3¶r3 = 3/r * 1/3r * S.A.\n4¶r2 = S.A.\n\nSphere Surface Area Formula:\nThe surface area SA of a sphere with radius r is 4¶r2.\nS.A. = 4¶r2
947383
cubes have all sides with the same length. Volume = length x width x height. So for a cube = length^3
205480
Surface area of a sphere is = 4 pi r^2\nThis means that surface area of a sphere is equal to 4 times the biggest circle in the sphere Or 4 times the area of the circle swept by its radius or 4 times the area of the base of its hemisphere.For example if the radius of a sphere is 1 unit then its surface area is = 4 pi square units.When it is divided by 4 it is equal to the area of the base its hemisphere.ie. area of the base of its hemisphere is = pi square units.
687221
A sphere can be formed by rotating a semi-circle about a diameter. \nLet us consider the circle x^2 + y^2 = r^2. \nIt is a circle with centre at the origin (0,0) and radius 'r'.\nIf the semi-circle of this circle which is above the x-axis is rotated by 360 degree about the x-axis (which is also a diameter) then a sphere of radius 'r' is produced. \n\nThe volume 'V' of any solid produced by revolution of the portion of the curve y=f(x) between x=a and x=b is \nV = pi*I(y)^2*dx in limits x=a to x=b\n[where 'I' denotes the integral sign]\n \n\nIn this case y^2 = r^2 - x^2 and the curve rotated is semicircle above x-axis so a = -r and b = r\n\nSo volume of the sphere is\nV = pi*I(y)^2*dx \n= pi*I[r^2 - x^2]dx in limits x=-r to x=r\n= pi*I[r^2]dx - pi*I[x^2]dx in limits x=-r to x=r\n= pi*r^2*x - pi*x^3/3 in limits x=-r to x=r\n= [pi*r^2*r - pi*r^3/3] - [pi*r^2*(-r) - pi*(-r)^3/3]\n= 4*pi*r^3/3
218464
If by area you mean "Surface area" then\nSA(sphere) = 4(pi)(r)^2\nand\nV(sphere) = 4(pi)(r)^3/3\n\nSince SA = 196 cm^2, then\n\n196cm^n = 4(pi)r^2\nr^2 = 49/pi\nr = 7/sqrt(pi) or approx. 3.949 cm\n\nfor the volume,\nV = 4(pi)(r)^3/3\nV = 4(pi)(7/pi^0.5)^3/3\nV = (4pi/3)(343/pi^1.5)\nV = (1372/(3pi^.5)) or approx. 258.02 cm^3\n\n^_^ Hope this helps ^_^
4519
(4/3)*pi*r^3\n\n[four thirds pi r cubed]\n\ngood luck!
635866
I might be missing something, but the cubic space something occupies is also referred to as it volume, where:\n\nfor a six sides regular box shape volume = heightxbreadthx depth\n\n( make sure all your measurements are in feet eg 1 foot 5 inches is 1 and 5/12 feet. \n\nHowever this formula is not true for a sphere or a trapezoidal box or a pyramid.  For whcih I'd recommend wikipedia or the old maths textbook as its hmmm, err 18 years since I last did all that stuff.
576160
v=3&#92;4 squared times 3.14 and divided by two sense it's half a sphere
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.
200332
This is the formula for the volume of a triangular prism.  Volume = Area of base x height.  ab/2 is the area of the triangular base, and multiplying by h (height) gives you the volume.
907361
4/3(3.14)0.01^3=4.186 ^-6