2)The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of th
612367
Volume of cylinder = Area of the base X height = πr2h.
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D.  Based on the ideal gas law, PV=nRT\n\nSolve for R to get: R = (P*V)/(n*T)\n\nfor two different conditions, then, you would have:\n\n(P1*V1)/(n1*T1) = R = (P2*V2)/(n2*T2)  or,\n\n(P1*V1)/(n1*T1) = (P2*V2)/(n2*T2)\n\nor P1*V1*n2*T2 = P2*V2*n1*T1\n\nNote how V1 and T1 can never be in the numerator together?  \n\nIn order for the ratio to work, one must be the numerator, the other the denominator, because volume is directly proportional to temperature -- the higher the temperature (keeping number of moles and pressure equal), the larger the volume.
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Cylinder: (pi)*(radius^2)*(height)\nPrism: (area of the base)*(height)
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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.
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Cylinder = PI r^2 x 6 r = 6PI r^3\nBalls = 4/3 x PI r^3 x 3 = 4 PI r^3\nratio = 4 PI r^3 / 6 PI r^3 = 4/6\n\nRatio = 2/3 of the space is used by the balls.
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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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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.
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r=radius\nd=diameter\n\n1 C=2r(pi)\n2 C=d(pi)\n\n(Same thing because 2r=d)
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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.
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The volume of a sphere with radius r is (4/3)pi * r^3. Your radius is 7yds, so the volume is (4/3) pi (7yd)^3 = (4/3)(343)(pi) yd^3 = 457 1/3 (pi) yd^3
970283
Your basic equation for volume is \nV = Pi * R^2 * H        (this is the answer to part B)\nIf you put the values for radius and hight into that equation you have\nV = Pi * 4 * 6\nWe know Pi is 3.14159, so the equation solves\nV = 75.39822369\nI think you mistyped the 6 when aiming at the 9.\n\nYour constant is Pi.\n\nPutting the values for R=3 and H = 5 into that equation will get \nV = Pi * 3^2 * 5\nV = 3.14159 * 9 * 5\nV = 141.372
438041
Since they r similar,\n\nDivide the Area of the larger cylinder by the smaller one,\n49(3.142)/25(3.142) to receive proportionality\n\n= 1.96\n\nTherefore 1.96 * volume smaller cylinder,\n\n1.96*50(3.142) = 307.8 = 98(3.142) [The Volume of the larger cylinder]
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1. obtain formulas for surface area and volume of cylinder\n2. let volume equal 1000 and solve this volume equation for h\n3. substitute the expression from previous step into surface area    equation to get equation with only r's\n4. differentiate surface area formula with respect to r set this equal to 0 and solve for r i got   r=10/3rd root(pi)\n5. substitute value for r into volume equation solve for h  i got h=10/(pi)^(2/3)\n\nincidentally, i used 2nd derivative test to conclude r is minimum\n\n\n\ni'll get back to u with more
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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.
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The volume of a cone is 1/3(Area of Base)(height) = 1/3 π r2 h
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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.
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Given that the volume of the cylindrical can is 100 cm^2...\n\n100 = (pi)r^2h\n\ndivide both sides by (pi)r^2 to isolate h\n\nh = 100/(pi)r^2\n\nSo, if the radius is 2 cm...\n\nh = 100/((pi)*4) - r^2 = 2^2 = 4\n\nh = 7.96 cm, rounded to first two decimal places, using 3.14 as the value for pi.