What is the formula to find the volume of a triangular prism?
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Here is instructions on finding the volume of any prisim.\n\nhttp://www.math.com/school/subject3/lessons/S3U4L2DP.html
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The area of the equilateral triangle is:\n\nA = 0.433 s^2\n\nA = 0.433 (10 ft)^2\n\nA = 43.3 ft^2\n\nThe volume of the pyramid is:\n\nV = 1/3 A h\n\nV = 1/3 (43.3 ft^2) (6 ft)\n\nV = 86.6 ft^3
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Find the area of the triangular base, then multiply that by (1/3) times height.\nThe formula is (1/3)*(area of base)*(height)\nSay the triangular base has base = 3 and height 4.\nArea of triangle = (1/2)(3)(4) = 6\nSay the height of the pyramid is 10.\nThe volume is  \n(1/3)(6)(10) = 20
362150
If I'm picturing this right, your solid looks like a triangle when looking at it from the z direction, but like half a cone (albeit a slanted cone with a side perpendicular to the base) when looking at it from the x direction.  If so, then we can use an integral to find the volume.\n\nIf we take slices in the x direction, we're looking at the volume of a half of a cylinder.  Since the volume of a cylinder is pi*r^2*h, and the cross sections are only semicircles, the volume of our slices is really (1/2)pi*r^2*h.\n\nOur height h is dx, since we're slicing perpendicular to the x-axis.\n\nWe have a diameter for our circle given by the equation for the upper bound - x + 2y = 8.  Rewritten in slope-intercept form, we have y = -x/2 + 4.  Since we need the radius for our integral, we take half of this: y = -x/4 + 2.  So our integral becomes (using S as the integration symbol):\n\nV = S (1/2)pi*(-x/4 + 2)^2 dx\n\nAdditionally, we're evaluating from x = 0 to x = 8, the point where the line meets the x-axis.  So,\n\nV = (1/2)pi S [(x^2)/16 - x + 4] dx\n= (1/2)pi[(x^3)/48- (x^2)/2 + 4x]\n= pi[(x^3)/96 - (x^2)/4 + 2x]\n\nEvaluating from 0 to 8,\n= pi{[(8^3)/96 - (8^2)/4 + 2(8)] - [(0^3)/96 - (0^2)/4 + 2(0)]}\n= 16pi/3
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find the area of the cross section.... then times the area by the length... that is of course if it's a prism
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180\n\nmade up of\n54 - 2 cube prisms\n27 - 3 cube prisms\n36 - 4 cube prisms\n36 - 6 cube prisms\n9 - 9 cube prisms\n12 - 12 cube prisms\n6 - 18 cube prisms
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Since you said ratio of a:b:c, not sides equal a, b and c, there is a formula, and of course a, b and c must be given. Given a, b and c, find their product. Divide the desired volume V by the product and take the cube root X of the result. Multiply a, b and c by X. The result is the 3 sides of the box with volume V.\nExpressed algebraically, \nX=(V/(a*b*c))^(1/3)\na1=a*X, b1=b*X, c1=c*X\n\nExample: I want a box with sides in the ratio 2:3:7 and volume = 65.2. \n2 * 3 * 7 = 42\n65.2/42 = 1.552381\n1.552381^(1/3) = 1.157887\n1.157887 * [2, 3, 7] = [2.315773, 3.47366, 8.105207]\n2.315773 * 3.47366 * 8.105207 = 65.19999
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Surface Area=sqrt{3}a^2\n    Volume =(1/12)sqrt(2)a^3\nhttp://en.wikipedia.org/wiki/Tetrahedron
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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.
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Volume = pi*r^2*h\n\nWhere pi = 3.14.159...\nr = raduis of cylinder in feet\nh = height of cylinder in feet
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V=(4/3)*pi*r^3\n\nwhere r is the radius of the sphere and V is volume.
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you split it into 2 ,a cone and a cylinder. first u need the slanting height of the cone and you find this by pythagorus theory for triangles ie L2 = h2 + r2, so height=6(found by subtracting the 15 from 21) radius=10 (20/2)therefore L2=6x6+10x10=136 therefore L =sqr root of 136 =11.6 surface area is A=pi*r*L\npi=3.142 so 3.142*10*11.6 = 364.5sq ft now the cylinder the surface area of a cylinder is circumference × h, or 2πr × h\nso 2*3.142*10*15 =942.6 so 942.6+364.5=1307.1 sq ft to find quantity of tins 1307.1/250=5.2 so they need 6 full tins you must check the formulas and calculations as I may have made a mistake ok
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use the formulas your given\nto find the volume of the cylinder\nthen pretend the semi hemi on  the top is a sphere find the volume and multiply by 1/2\n\nadd two totals to find volume
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Volume of cylinder = area of base * height.\nSince the base is a circle, that part is Pi *r^2\nSo we have Pi * r^2 * height --> \n3.14 * 12^2 * 21 = ?\n\nVolume of square prism = area of base * height\nSince the base is a square, that part is side^2\nSo we have 12 * 12 * 21 = ? \n\nSubtract the results for your final answer.
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This is not tricky at all. The volume is 1-1/2 cylinders of "height" 50,000 meters and radius 4 meters.\n\nThe formula for the volume of a cylinder is\n\nV = pi * r^2 * h
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Base times height gives the volume of the prism.\nVolume of prramid= 1/3 x base x height =1/3 x 24=8 cubic inches.
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Area of rectangle = length x width \nArea of a circle = pi x R x R = pi R^2 where pi~3.14 and R - radius\nArea of an ellipse = pi x a x b see http://www.tpub.com/content/engineering/14069/css/14069_33.htm \n\nVolume = area of the base times hight\nVolume of a rectangular prism= area of rectangle x height = length x width x height\nVolume of a sphere = (4/3)pi x R x R x R = (4/3)pi x R^3\n \nCheck math tables or the web for equation of other geometric figures \n\nPercentage = 100 x (partial amount) / (total amount)\n\nHave fun