A cylinder has a curved surface area of 4m2. If it has a radius of 70cm, what is the height and the volume?
396424
The curved surface area of the cylinder would be made up of the circumference times the height.  Figure the circumference then divide the surface area by that to get the height.  it would probably be best to convert M2 into cm2 first.  100 cm=1M so 1 sq m would be 100 x 100 or 10,000sq cm x 4m2 equals 40000 cm2.  The C would be 2(pi)r  which is 2 x 3.14 x 70 = 439.6 cm.  Divide 40,000 by 439.6 = 90.99 cm for the height. volume would be (pi)r2h or 3.14 x 4900 x 90.99 = 1399972 cu cm
410603
Well, one possibility is radius=3.3cm and height=8.3cm., this measure is proportional with a normal can. You have to remember that a can is a cylinder, so the dimensions must match with 3.141592*r^2 * h=280 - 285
975805
1. A sphere with a diameter of 16 mm has the same surface area as the total surface area of a right cylinder with the base diameter equal to the sphere diameter. how high is the cylinder?\nA (sphere)=4*pi*r^2=4*pi*8^2=256*pi mm^2\nA cylinder=2*pi*r^2+2*pi*r*h==128*pi+16*pi*h\nA sphere=A cyl\n256*pi=128*pi+16*pi*h\n128*pi=16*pi*h\n8=h\nheight is 8 mm\n\n2. find the volume of a frustum of a right pyramid whose lower base is a square with a side 5 in. , whose upper base is a square with a side 3 in. , and whose altitude is 12 in.?\n\nB1 area=25in^2\nB2 area=9in^2\naltitude=3\nV=1/3(3)(25+15+9)=49in^2\n\n3. The figure formed by the intersection of a solid with a plane parallel to the base of the solid is congruent to the base if the solid is a........? \n\nprism
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
819179
1)  the answer is h/r =2 or 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). This ratio of h/r that minimizes SA is independent of the volume though of course h and r are not independent of the volume.\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\nYou are given the volume of the tins as 1 liter\n\n1000 = pi r^2 h,  but h=2r\n\n1000= 2 pi r^3 so r = (1000/2pi)^1/3 = 12.62 cm approx\nand h= 25.24 cm\n\n2) The answer is h/r = 8/pi\n\nIn this case your you have waste metal.\n\n2r is the diameter of the top of the tin. If the top and bottom are cut out of the square then the square will have to have an area of (2r)^2 = 4r^2. So the area A of material required for the tin is now: \n\n(1)   A = 2(4 r^2) +  2 pi r h  since the top and bottom are cut from squares.The procedure is the same in determining h/r, just a different function for the area of aluminum required\n\nAgain use V = 1 and so h = 1/(pi r^2)\n\nSubstituting this value of h in the above equation gives:\n\nA = 8r^2 + 2/r \n\ndA /dr = 16r -2/r^2\n\ndA/dr =0 when 16r = 2/r^2\n\nr^3 = 1/8 so r = 1/2 and h = 1/(pi r^2) = 4/pi\n\nSo h/r = 8/pi\n\nNow that you have the ratio h/r, you can determine the values of h and r when the volume of the can = 1000 cm^3\n\nNotice the value of h/r in this case is a little higher than in the no aluminum waste case. Of course, that makes sense\n\n3) This is also true for the equilateral triangle and hexagon\nYou need to determine the area of the equilateral triangle and hexagon having a maximum inscribed circle of radius r. The inscribed cirlcle will touch the midpoints of the edges of the regular polygon. We saw for the square this was 4 r^2. The general formula for the area of a regular polygon having N sides, in terms of r (its inradius, i.e. apothem) is:\n\nArea = r^2 x N x tan(pi / N)\n\nFor equilateral triangle N =3. For a hexagon, N=6. Plug these values in this formula and it will give you the area in terms of r When you calculate it, make sure your calculator is using radian measure, not degrees. So the area of aluminum required for the for the can if the top and bottom are cut from a regular polygon having N sides is\n\nA = 2 r^2 x N x tan(pi/N) + 2/r\n\nDetermine d A/dr. Set it equal to 0 and solve for r, and then solve for h.\n\nHere's a link about the Area of regular polygons.\n\nhttp://www.mathopenref.com/polygonregulararea.html
96858
erm the volume of the circle would be the same, the volume of the cylinder would be (pi)r*r*h (r=radius, h=height)
114607
Is 4ft the radius or the diameter? (diameter is twice the radius).  Use the formula 2 x 22/7 x r  OR 22/7 x d (both of which are the same since 2r=d)
421815
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.
747001
I'm assuming you are familiar with calculus.  Consider an infinitesimal cylinder at height 'y' of thickness 'dy'.  The surface area of that cylinder is 2*pi*Radius*thickness.  Here the radius is simply 3e^2y, and 'dA' the infinitesimal area is given by 2*pi*3e^2y*dy.  To get the total area gotten by rotating this curve, (note we don't have to do any rotation as its already factored in by the assuming an infinitesimal cylinder) simply integrate between 0-3 the above expression, which I leave as an excercise for you.  Hope this helps.
522898
Imagine you unraveled the cylinder, the middle would turn into a rectangle, right? so to find the surface area, take the height of the cylinder and multiply it by the circumference of the circles at the bases, then add in the area of the circles. Circumference is 2(pi)r and area is (pi)r^2.
486266
the formula for volume of a cylinder is V = h * pi * r^2.\nAlternatively, the surface area is A = h * pi * r * 2.\n\nSo, if you have either the surface area or the volume, you can calculate for the height.\n\nH = Volume / pi * r^2\nH = Area / pi * r * 2
784010
Take the formula for the surface area(S) and solve for r\nS=4*pi*r^2\nr^2 = S/(4pi)\nr =squareroot(S/4pi) or (S/4pi)^(1/2)\n\nNow take the formula for the volume\n4/3*pi*r^3\nand substitute the formula for r into the equation\n4/3*pi*(squareroot(S/4pi))^3\n4/3*pi(S/4pi)^(3/2)
866787
let the radius of the cylinder be x,  drawing a cylinder in a cone on the paper, we see 2 triangles - the cone & the triangle with it's base as the top flat surface of the cylinder. follow me?\n\nif u do, then let's assume the height of the second triangle to be y. y can be found in terms of x as:\n(since both triangles are similar)\n\nx:4 :: y:12  \ni.e. x/4 = y/12\n=> y=3x\nthus ht of cylinder = ht of cone - y\n=12-3x\n\nvolume of cylinder = pi*r2*h  (r-> radius, h-> height of cylinder)\nv= pi * x2 * (12-3x) = pi * (12x2 - 3x3)\n  (the second term being 12 *x*x - 3*x*x*x ....sorry, i don't have a math equation display software here)\n\npartialy differentiate above equation wth respect to  x, we then get\ndv/dx = pi * (24*x - 9*x*x)\n\nequating dv/dx to zero, (to find a value of x that makes the volume value either maxium or minimum. u can verify it's max by again differentiating dv/dx with respect to x, equating to zero & finding if the value solved for is positive or negative)\n\nanyways, we get\n\neliminating  pi,\n24*x - 9*x*x=0\n\n=> x=24/9 = 8/3= 2.67\n\nnow, simply substitute this value of x in the volume equatiion above to get\n v= pi * (12*2.67*2.67 - 3*2.67*2.67*2.67)\n= 89.372 or so.\n\n\nuh...i guess i only confused u up, hope it helped u atleast a bit.
919539
Area =pi (Radius)^2 = 22/7(3)^2 =22(9)/7 = 28.29 ft^2 Ans.
612367
Volume of cylinder = Area of the base X height = πr2h.
624334
Example: Find the length of a helix which winds three times around a cylinder of height 12" and radius 3"\n\nAnswer: divide the cylinder into three sections. The helix goes once around a cylinder of height 4" and radius 3"\n\nThe surface of the cylinder can be "peeled" into a rectangle 4" by 2 * pi * 3" = 18.850". The helix is a diagonal of that rectangle. So its length is sqt(4^2 + 18.850^2) = 19.27"\n\nIt goes around the cylinder three times and its total length is therefore 57.81"
246604
The volume of a cylinder equals the area of the base times the height.  The area of the base equals pi times the radius squared.\n\nSo first you need to find out the area of the base. \nBase equals pi times radius squared.\npi = 3.14\nyour radius is 3 inches\nSquare your radius first.  3 squared = nine\nthen multiply by 3.14\nnine times 3.14 = 28.26\nNow, your base is 28.26\nSo multiply your base times your height.  Which would be \nBase = 28.26 inches x Height 6 inches = 169.56 cubic inches\nAnswer is 169.56 cubic inches