how do you find the volume and the surface area of a cone?
543695
volume = (1/3) b h = 1/3 pi r 2 h \nSurface area = pr2 + prs\ns= the height of the outside of the cone, while h = the height of the cone at its center
533954
The surface are of the cone is a segment of a circle.\n\nThe circle has radius equal to the slant height of the cone (20 cm).\n\nThe circumference of the circle is 2 x 20 x 3.14 cm = 125.66 cm\n\nSince the perimeter of the base of the cone is an arc on that  circle, and you have given it as 314 cm, the cone can't exist.\n\nAre you sure that the base perimeter isn't 31.4 cm?\n\nIn that case the arc of the circle would have length 10 x pi cm, the whole circle would have circumference 40 x pi cm, the arc would be 1/4 of the circle, and the surface area of the cone would come out to be 1/4 the circle, (1/4) x 400 x pi = 314.\n\nNote to cvokhai below: Can you sketch a cone with a slant height of 20 and a radius of 50? I can't.
970422
The solution is too convoluted to put it here without diagrams and a good equation editor.  If you wish, I can email a Word document detailing the solution.  I figure that the cone is (1 + 2*sqrt(2/3) + sqrt(3))*r (about 4.365 r) high and has a base radius of ((sqrt(1/2) + sqrt(4/3) + sqrt(3/2))*r or about 3.087.
895037
surface area of a cube is 6a^2\nvolume=a^3\ntheir relation: V/SA = a/6\n\nif its cut into half, volume will be:\n(a/2) x a^2 = (a^3) / 2\nthe surface area will be 2a^2 + 4a(a/2) = 4a^2\nnow their relation: V/SA = a/8\n\nnote: crazy horse's answer went wrong when he assumed a halved cube has only two of its sides halved. in fact, it has its 4 sides halved.
430786
The formula for the capacity or volume, V, of a cylinder is:\n\nV = Π(d^2)h/4\nwhere:\nΠ = 3.1416 (value up to 4 decimal places)\nd = diameter of the cylinder\nh = height of the cylinder\n\nSo, merely substitute the values that you have and you will get the capacity or volume of the cylinder. Just make sure to use similar unit of measures both for the diameter and the height.
528597
Total Area = Base Area + Lateral Area\n\nLateral Area= pi x radius x height of the slant.\nHeigh of slant = sqrt(cone height^2 + radius^2)\n\nLateral Area = (pi)(r) * sqrt(cone height^2 + radius^2)\nBase Area = (pi)(r^2)\n\nTotal area = (pi)(r) * sqrt(cone height^2 + radius^2) + (pi)(r^2)
598391
First find the area of the circle that is on the top or bottom of the cylinder. The area formula for a circle is \n\n"pi,r squared. That means multiply pi times the radius of the circle which you have to square first.\nThen you take the number that you get and multiply it by the height of the cylinder.\nGood luck.
852456
Total surface area of a tin can = A = 2pr^2 + 2prh\nVolume of a tin can = V = pr^2h = 1000 cm^3\nTherefore, h = 1000 / pr^2\n\nSubstituting this into the area equation gives :\nA =  2pr^2 + 2pr * 1000 / pr^2\n= 2pr^2 + 2000 / r\n\nNow take the derivative of A with respect to r :\ndA / dr = 4pr - 2000 / r^2\n\nSet this equal to zero to find the minimum :\n4pr - 2000 / r^2 = 0\nThis can be rearranged to show that : 1000 / pr^2 = 2r, which equals h, as shown above.\nContinuing to find r, we get : r = (500 / p) ^ (1/3), or approx. 5.42 cm.\n\nNow h = 2r = 2 * (500 / p) ^ (1/3), or approx. 10.84 cm.\n\nThus, ratio is h / r = 2r / r = 2\n\nI'm a bit confused about the second question, but I think what you want is a square sheet of aluminium, such that all 3 pieces of a can will fit, with the minimum of wastage. This would be a square sheet with the dimensions : (perimeter of can) by (height + 2 * radius).\n\nThus, Perimeter = Height + 2 * Radius, because the sides of a square are equal.\nTherefore, 2*pi*r = h + 2r,\nso, h = 2r(pi - 1)\n\nBut, V = pi*r^2*h = 1000, so h = 1000 / (pi*r^2)\n\nEquating the 2 values for h gives :\n2r(pi - 1) = 1000 / (pi*r^2)\nfrom which we get : r  = {500 / [pi(pi - 1)]} ^ (1/3)\n\nSo now we know that h = 2r(pi - 1), so that after substituting for r, we get : \nh = 2 * (pi - 1) ^ (2/3) * (500 / pi) ^ (1/3)\nAnd we find that the ratio h / r = 2r(pi - 1) / r = 2(pi - 1)\n\nWell, that was a bit of speculation, but even if I've got it wrong, then perhaps you can adapt it to your needs.\n\nEdit\nCan't help feeling I've misunderstood the second question the first time around, but on re-reading it many times, I still don't understand it.
455520
volume for a cone (Mt. Everest) is: 1/3Bh (1/3 X Area of base X height). Find that and you might be able to find the mass.
125346
Use Heron's formula to find the area of the base: 6 times the square root of 5.  Then multiply that by the height.\n\nThe volume is 30 times the square root of 5.
991600
Volume cone = 1/3 pi r^2 h\n\nIf I get the picture you have almost complete cone with a 36" base and the height is 36", but the height would be greater if it was not missing the nose-cone which has a one inch diameter cross-section. Is that correct? If so put a footnote on your question. This is not difficult to determine but I want to know if I have it right. Also, be more specific about what you are after (doing) with the 1x1x2" pieces. it's easy to figure how many of these will 'fit' in the half cone, volume-wise, but if you are doing some kind of construction, the number of pieces required will be different. Anyways, I have to go out for a bit so if someone else does it for you, that's good. If not I'll take a look at it later.
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.
250763
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
315214
slant height = 12.08\ntotal surface area= 251.428\nvolume = 287.98
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.
520391
Area is given in square ft: Length * Width yields ft*ft=ft^2 =sqft\n\nVolume is given in cubic ft: L*W*Height yields ft*ft*ft=ft^3 =cuft\n\nThe formulas above are for area of a square or rectangle, and volume of these shapes in 3-dimensions.  \nFormulas for Area and Volume are different for circles, spheres, cylinders and such.\n\nArea of a circle = pi*(radius^2)\nVol of a sphere= (4/3)*pi*radius^3\nVol of a cylinder= pi*radius^2*Length
887520
Volume = pi r^2 h \n\nMeasure a Coke can to get r and h and calculate the volume.  Plug it in for V in  the volume formula and solve it for h.\n\nThen take the surface area formula, SA = 2 pi r^2 + 2 pi r h,\nreplace the h with your answer from above, find the first derivative d(SA)/dr, and make it equal to zero to find the minimum.