Determine the volume of a cylinder with radius 4 and height 7.?
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
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.
612367
Volume of cylinder = Area of the base X height = πr2h.
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.
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
969797
Let the radius of the sphere be R.\nLet x be the radius of the cylinder.\nThen height of half of the cylinder= sqrt(R^2-x^2)\n\nTotal surface area of cylinder = 2*pi*x^2 +2*pi*h, so\nS=2*pi*x^2 +2*pi*2*(R^2-x^2)^.5  [Eq I]\ndS/dx=4*pi*x + 4*pi*.5*(-2x)(R^2-x^2)^-.5\n=4*pi*x - 4*pi*x/(R^2-x^2)^.5\n=4*pi*x(R^2-x^2)-4*pi*x =0\nR^2-x^2-1=0\nx^2=R^2-1\nx=+ or - sqrt (R2-1)\nPlug these values of x into [EQ I] to get answer.
147975
First, find the volume of the can: [pi]r-squared x the height of the can. If the 3 balls in it each have a radius of 5 cm, then they are each 10 cm tall, and the can is 30 cm tall. So the volume of the can = [pi]x25x30 = 750[pi] cubic cm.\n\nNext, the volume of each ball is 4/3 x [pi]r-cubed, or 166.67[pi] cubic cm. Three of them would be 500[pi] cubic cm.\n\nLast, subtract the volume of the balls from the volume of the cylinder to get 250[pi] cubic cm, or about 785.4 cubic cm.
1000601
The method to finnd the volume of sphereis computed by The mathematician, Archimedes.\nThe formula for find the volume =4/3 pi  r cube\nie, pi = 3.14\n     r is the radius of the sphere.\nFor eg, r=1.2 m\n v =4/3 pi*(1.2*1.2*1.2) \n    =4/3*3.14*1728\n     =7.2346 cu.m\n     1 cu.m = 1000 litres\nV   =7.2346*1000\n       =7234.6\n\nDon't u understand.
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.
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.
1178530
Surface Area of a Cylinder = 2 pi r 2 + 2 pi r h\n\n\nr=radius\nh=height\n\nnote: the 2 after the 2 pi r is a square
809750
Ratio of what?\nSurface area?\nVolume?\n\nI will go with volume.\n\nassume radius of sphere is = 1\n\nsphere = 4/3pi\ncylinder = 2pi\ncone = 2/3 pi\n\neat the pi's (get rid of them) and multiply what's left by 1.5\n\nSphere:Cylinder:Cone = 2:3:1\n\nI hope that helps
872528
1.) The cylinder with the lowest surface area per unit volume will be cubelike. \n\nSurface area for a cylinder is 2πr^2 + 2πrh, where the 2πr^2 is for the base, and 2πrh is for the tube itself.\n\nOn a similar cube, the base would be 2 sides (top and bottom), and the tube would be remaining 4 sides. Thus, for a cubelike cylinder, 2πrh will equal 2 * 2πr^2 (since the tube accounts for twice the area as the base).\n\n2πrh = 2 * 2πr^2\nh = 2r (h/r = 2 for your ratio)\n\nV = πr^2h = 2πr^3\n1000 = 2πr^3\n500 / π = r^3 = 159.15\nr = 5.419 cm, so h = 10.838 cm\n\nSA = 2πr^2 + 2πrh = 2πr^2 + 4πr^2 = 6πr^2\n6πr^2 = 553.52 cm^2 \n\nCheck:\nr = 5.418\nV = πr^2h = 1000\nh = 1000 / π * (5.418 ^2) = 10.844\nSA = 2πr^2 + 2πrh = 2π (5.418 ^2) + 2π (5.418 * 10.844) = 553.60\n\nr = 5.42\nV = πr^2h = 1000\nh = 1000 / π * (5.42 ^2) = 10.836\nSA = 2πr^2 + 2πrh = 2π (5.42 ^2) + 2π (5.42 * 10.836) = 553.56\n\nWithout the diagram, it'll be hard to answer 2 and 3.
137325
This is a lot to ask here. Why dont you look it up? \n\nAnd a lot of these are easy to figure out. \n\nSphere surface area is A=4 *pi *R^2 where R is the radius\n\nbecause A={int 0 to 2 pi} {int 0 t0 pi} R^2 sin(a)dadb\n\n\nThe cube surface area is A=6*S^2, where S is the length of an edge because there are 6 sides, each of area A^2.\n\nThe cylinder surface area A=2*pi*(R^2)+2*pi*R*H, where R is radius and H is height, because it has two circular end caps of area pi*(R^2) and a side of dimensions 2*pi*R by H, when it is unrolled. \n\nCone surface areas can be found the same way. Just unroll the side, and you get a triangle with height sqrt(H^2+R^2) and base 2*pi*R. The area of a triangle is .5*base*height. Then add in the area of the round bottom. \n\nAnd so on. I am sure you can do this yourself.
796580
Yes, the answer is h = 2r\n\nThis is a classic optimization problem. You want the minimum surface area(SA) for a cylindrical shaped tin for a fixed Volume(V)\n\n(1) SA = 2pi r^2 + 2pi r h\n\nV = pi r^2 h (for simplicity set V = 1)\n\nso (2)    h = 1/(pi r^2)\n\nSubstituting this value for h into (1) gives:\n\nSA = 2pi r^2 + 2/r\n\nd/dr SA = 4pi r - 2/r^2\n\nd/dr SA = 0 when 2/r^2 = 4pi r\n\nthat is: (3)   r = 1/(2 pi r^2)\n\nTo get the value of the ratio h/r divide equation (2) by equation (3), which yields a value of 2 to 1.\n\nh = 2r
411206
Let R and H be the radius and altitude of the CONE\nLet r and h be the radius and altitude of the CYLINDER\nVc=Vol of Cylinder\n\nThen Vc = pi*r^2*h\n\nIf the radius of the cylinder is zero (r=0), its altitude is the height of the cone (h=H).\n\nIf the radius of the cylinder is the same than the radius of the cone (r=R), its altitude is zero (h=0).\n\nFrom the above conclude:\n\nh=H when r=0   and   h=0 when r=R\n\nTreat h as a dependent variable (y) and r as an independent variable (x). Then, the slope of the cone (from the line above) is:\n\n(H-0)/(0-R) = -H/R\n\nTherefore the altitude of the cylinder "h" (the dependent variable) as a function its radius "r" (the independent variable) is:\n\nh=H-(H/R)r\n\nPlug this "h" variable in the formula of Vc\n\nVc = pi*r^2(H-(H/R)r)\n\nCompute the derivative of this function with respect to r (the independent variable. Remember H and are unknown but constants) and equate to zero. Next solve for r.\n\nr=0 (would yield a minimum)\n\nr=(2/3)R is the maximum\n\nPlug this value in the formula of "h" given above to obtain:\n\nh=H/3\n\nPlug this two values of r and h in the original formula Vc and obtain YOUR ANSWER:\n\n(4/27)*pi*H*R^2\n\nCompare to the volume of the cone, a little less than half of it.
544209
Assuming that the column of Hg is a cylinder with a base with radius 5, and volume unkown, we can use the equation for the volume of a cylinder to determine how high it must be. But remember the high is dependent on the radius of tha base.\n\n760 mmHg = 101,325.024 Pa\n\nPa = [F]/{A] = N/m^2\n\n101,325.024 [Pa] = (1.36x10^4 [kg]/[m^3] * 9.81 [m]/[s^2]\n* [volume][m^3])/(78.53[m^2])\n\nUnits:\n\n[Pa] = [Pa]\n\nvolume = 59.64 m^3\n\nvolume = [pi][r^2][H]\n\n59.64 m^3 = [pi][25m^2][H]\n\nH = 2.3856 m