what is the formula for the volume of a prism?
549879
haha I was just working on my geometry homework and we're doing that right now.. the formula for the volume of a prism is: V=Bh, where B=the area of the base and h=the height of the prism.. that's the equation for ALL prisms..\n\nthe equation for the volume of a cylinder is V=pi(r^2)h\nso it's pi times the radius squared times the height\n\nthe equation for the circumference of a circle is C=2(pi)r\nso 2 times pi times the radius
691753
maybe a hexagonal prism http://en.wikipedia.org/wiki/Hexagonal_prism http://en.wikipedia.org/wiki/Prism_%28geometry%29
10703
Volume of a pyramid = (1/3)(area of base, which is a square) * height\nSo 30cm^3 = (1/3) (s^2)(h) Multiply by 3 to clear the fraction --> \n90cm^2 = s^2(h)\n\nNow the problem is that we have one equation for two unknowns. We cannot arrive at one definite solution because there are infinite possibilities. \nSo we can get some possible dimensions by assigning a value to one dimension and then working out the other one. \n\nFor example, if the sides of the botom are 1 cm, then the height is 90\nIf the sides are each 3, then the area of the base is 9 and the height is 10.
563210
The volume of a pyramid is equal to one-third the base area multiplied by the height.\n\n\nImagine a step-pyramid made up of small square prisms with dimensions\na-by-a-by-b, arranged in square layers. If the layers are k-by-k for\nk = 1, 2, 3, ..., n, then the total volume of the step-pyramid is:\n\n   V = a^2*b*[1^2 + 2^2 + 3^2 + ... + n^2],\n     = a^2*b*n*(n + 1)*(2*n + 1)/6 (which can be proved by induction),\n     = a^2*b*n^3*(1/3 + 1/[2*n] + 1/[6*n^2]).\n\nNow, the height of the step-pyramid is h = b*n, and the area of the \nbase is:\n\n   B = a^2*n^2, \n\nso the volume is:\n\n   V = h*B*(1/3 + 1/[2*n] + 1/n^2).\n\nNow let n -> infinity, so the steps get smaller and smaller, and the\nvolume of the step-pyramid approaches the volume of the inscribed \npyramid. Then the right-hand side approaches h*B/3, as the volume V \napproaches the volume of the pyramid.\n\nThis same proof works for a pyramid with any polygonal base. For a \ncone, take a pyramid with a regular m-gon for a base, and let \nm -> infinity.\n\nThe base approaches a circle, and the pyramid approaches a cone, and \nthe formula V = h*B/3 still holds in the limit.\n\nThere is another proof, which cuts a rectangular solid into six pieces \nof equal volume, each of which is a triangular pyramid (or irregular\ntetrahedron). This proves that the volume of each is 1/6th the volume \nof the starting rectangular solid, and each has base of area 1/2 the \narea of one of the faces of the solid, and height equal to the \ndimension of the solid perpendicular to that face
360723
Use a prism like Newton did.
784010
Take the formula for the surface area(S) and solve for r\nS=4*pi*r^2\nr^2 = S/(4pi)\nr =squareroot(S/4pi) or (S/4pi)^(1/2)\n\nNow take the formula for the volume\n4/3*pi*r^3\nand substitute the formula for r into the equation\n4/3*pi*(squareroot(S/4pi))^3\n4/3*pi(S/4pi)^(3/2)
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.
175713
Your question is too complicated to appreciate the math in it, which is supposed to be the real beauty in the first place. Anyway, I have tried figuring it out and come with equations. I do not even want to try and begin substitution and end up with more complications. I just thought once you saw the relation, you would throw those 10 points my way.\n\nAssuming a to be sides of the squares of the prism and b to be the length of the rectangles, we know that the sum of all dimensions is 14a+5b. Now I do not even want to get started why you brought it the story of the equilateral triangle. You can just say the sum  of the dimensions is 61. Anyway, since any side of the trianle, as it is equiangular hence equilateral, is twice 14a+5b and 122, the sum of the dimensions will be 61. So your first equation is 14a+5b=61\n\nYou know the volume of the prism is the length X width X heiht = a x a x b = (a^2)b This is equal to the surface area. The surface area is the sum of all the areas on the prism and that is a^2+4ab. (How about you calculate how that came up?)\n\nSo there is your second equation, (a^2)b = a^2+4ab So then from 14a+5b=61, express a in terms of b or the other way around and plug it into the second equation and experience brutal complications and figure out what the variables are. I think you know it is too easy to calculate each dimension and area after that.
46232
The volume of the pyramid is 1/3 the volume of the prism.\n\nTo prove this, look at a horizontal cross section of pyramid. Let A = the area of the base.\n\n\nIf the the height of the pyramid is h, look at a cross section of the pyramid at a height t above the base. Any one dimentional measurement x in the base, will have size x(h-t)/n in the cross section. Any two dimensional measurement, (area) will be multiplied by ((h-t)/h)^2, i.e. A((h-t)/h)^2.\n\nNote\nNow integrate for t = 0 to h, A((h-t)/h)^2 dt\n\nYou get -A/3(h - t )^3/h^2.\nEvaluating at t = 0 and t = h you get 1/3Ah.\n\nThe volume of the prism is Ah.
448895
Volume, V = 2πrh...\n\nSince there is only one equation, but two unknowns...\n\nyou must supply the value of one unknown (you must decide on a pre-determined value. You either decide the value for the radius of the cylinder or its height) to solve for the other dimension.
121103
The formula for the volume of a pyramid is V = (1/3)Ah\nwhere A is the area of the base, h is the height, and V is the volume \nof the pyramid.
174332
The surface area of a sphere is A=4*pi*r^2 where r is the radius of the sphere. The *volume* is (4/3)*pi*r^3.
419817
deviation= (refractive index -1)*angle of prism\n\nif prism angle is small...\nand\ndependence of rf with wavelength is given by cauchy's formula\n\nrf= A/wavelength....  A is constant\n\nso dependence (deviation) proportional to [(1/wavelength) -1)]
458187
find the area of the base and multiply it by the height\n\n(1/2)*b*h1*h2  for a triangular prism h1 is height of the triangle, h2 is the height of the prism\n\npi*(r^2)*h for cylinder, h is height, r is radius of the base
466950
Volume = Area x height\nArea = r x r x pi\npi is approximated by the fraction 22/7\nTherefore Volume of cylinder = 4 x4 x 22/7 x7 = 352 units^3
359961
Find the areas of all 6 faces of the rectangular solid by muliplying each one's width by length.  Then add them together for the total surface area.  To find volume, multiply length by width by height.  The ratio will be the total surface area divided by the volume (or expressed as a fraction the total surface area over the volume).
116020
Volume = pi*r^2*h\n\nWhere pi = 3.14.159...\nr = raduis of cylinder in feet\nh = height of cylinder in feet