how do you find ratio of surface area to volume in a rectangular prism?
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).
663486
Diagram here:\n\nhttp://mathworld.wolfram.com/TriangularPrism.html\n\nto solve for its volume, calculate for the area of the triangle bottom and multiply it by the height of the prism.\n\nTo compute for surface area, compute for the area of the 3 rectangular faces and add the area of the 2 triangular faces.
559607
A rectangular prism is simply made up of 6 rectangles.  One pair of rectangles would be 3cm x 3cm (the ends).  The other 4 rectangles would be 3cm x 20cm.  So the total surface area would be the sum.\n\n3cm x 3cm = 9 sq. cm\n3cm x 20cm = 60 sq. cm\n\nSo 9 + 9 + 60 + 60 + 60 + 60 = 258 sq. cm.\n\nIn this case two of the dimensions were the same, but if the sides were h,w,l the total surface area would be:\n= hw + hw + hl + hl + lw + lw\n= 2hw + 2hl + 2lw\n= 2 (hw + hl + lw)\n\nIn your example:\n= 2 (3x3 + 3x20 + 3x20)\n= 2 (129)\n= 258 sq. cm.   (Don't forget the units are sq. cm)
212343
I can't imagine finding the surface area from just the volume without knowing the SHAPE OF THE OBJECT.
84844
Height = H = 10"\nRadius = r = 4"\n\nVOLUME (not area, volume is 3-dimensional) = (π/3)(r^2*H) = (160/3)*π\n\nSURFACE AREA = (πr)(sqrt(r^2+H^2)) = 4(sqrt(116))*pi
553954
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.
287728
Surface Area = [Base Area] +\n1/2 × Perimeter × [Side Length]\n\nVolume = 1/3 × [Base Area] × Height\n\nThe Surface Area has two parts: the area of the sides (the Lateral Area) and the area of the base (the Base Area). \n\nThe Base Area depends on the shape, there are different formulas for triangle, square, etc. \n\nBut the Lateral Area is surprisingly simple. Just multiply the perimeter by the side length and divide by 2. This is because the sides are always triangles and the triangle formula is base times height divided by 2
937032
I'm assuming:\nThe box has a square top and bottom.\nThe volume v is fixed.\nr is the length of a side of the top.\nh is the height of the box.\n\nv = r^2*h\nh = v/r^2\n\nThe surface area is a top and bottom both r x r and\nthe sides which are r x h.\n\nArea = 2*r^2 + 4*r*h = 2^r^2 + 4*r(v/r^2) = 2r^2 +4v/r\n\ndA/dr = 4r -4v/r^2\n\nSet to 0 and solve\n0 = 4r -4v/r^2\n\n0 = 4r^3 -4v\n0 = r^3 - v\nv = r^3, or  r = v^(1/3)\nThat means that the container is a cube.
198865
Volume = (area of the base) x (height)
182640
I'm not sure if this is what you're asking, but if...\nd = length\nd-3 = width\n\nthen the area is d(d-3), a.k.a. d^2 - 3d .\n\nHope this helps!
913838
A rectangular prism is like a box. So it has 6 sides in 3 matching pairs: top and bottom, right and left sides, and front and back. You can find the area of each pair and add them together:\nABxBC+ABxBC+BCxCD+BCxCD+CAxCD+CAxCD = PA (Prism Area)\n\nOr you could get the areas of one of each pair and double it:\n2x(ABxBC+BCxCD+CAxCD)=PA (Prism Area)\n\n;-D AB is the length of the front left side, with A at the bottom left corner, B at the top left corner. BC is the length of the front top with C at the top right corner, and CD is the length of the depth, with D at the back right corner.
67968
It is similar to calculating the area. \n\nIt is a product of Length and Width (L x W).
1124064
Because you have a fixed height, h, of 30m, and the Volume  of a triangular prism is given by: V = h*A where A is the area of the triangular base, your problem reduces to maximizing A, given the perimeter of A = 210m\nAn equilateral will enclose the maximum area(see link below) So the length of each side will be 210/3 = 70 m. The area of an equilateral triangle =  S^2 x sqrt(3)/4 where S = side length. So, in your case the area = 70^2*sqrt(3)/4 = 2,121.18 m^2 and the maximum volume for your prism is 30m*2121.18 m^2 = 63,652.86 m^3\n\nFor a polygon, the general rule is: the 'closer' the shape of a polygon is to a circle, the greater the area of the interior of the polygon. This implies that a equilateral triangle, a square(see below), a regular pentagon; and in general a regular n-gon will enclose the most area. \n\nConsider a square with side length X, then the area of the square = X^2 and the perimeter is 4X. Let's keep the perimeter fixed at 4X and see what happens to the area if we let one pair of opposing sides of the rectangle be X-y and the other two be X+y (Note the perimeter will still be 4X). However, the area is now: (X+y)*(X-y) = X^2 - y^2. We see that if y>0 then area decreases, while the perimeter stays the same. We see that a square encloses the maximum area for a fixed perimeter. \n\nHowever, if you allow the height, h, to vary as well then you have 3D maximization problem; but the solution is not difficult in this case either. In general, right-angle prisms with regular polygon bases will have a maximum volume for a fixed perimeter or surface area\n\nhttp://mathforum.org/library/drmath/view/53789.html\n\nhttp://mathworld.wolfram.com/Prism.html\n\nhttp://mathworld.wolfram.com/EquilateralTriangle.html
918429
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
856302
Surface Area = (2 •  p   • r²) + (2 • p  • r • height)\n\nWhere (2 • p • r² ) is the surface area of the "ends" and\n(2 • p • r • height) is the lateral area (the area of the "side").\n\nVolume   =   p • r² • height   =   ¼ • p • d² • height\n\np = Pi
192399
In the front?  You have to consider the whole cube to find volume.  Volume = base area * height  You could find the surface area of one side, but you'd need to know the side length.
254095
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