what is the formula for finding the volume of a cone?
543954
1/3 x pie x radius (power of 2) x height
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
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
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.
587102
Volume of water in the cone is therefore 200cm3. When x number of spheres are added, the volumes decresese by 1/4 which means 50cm3. volume displaced is equal to the volume of the solid immersed. therefore x.1/2 = 50. x=100.\n\nur volume of sphere is 1/2 not 1.
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The area of segment of a circle is given by\nA = r^2[theta - sin(theta)]/2\n\ntheta is given by\ntheta = 2 arcsin(c/[2r])\n\nwhere c is the chord length and r is the radius.  So,\ntheta = 2 arcsin(c/[2r])\n= 2 arcsin(20/[2(12)])\n= 1.97 radians\n\nSo the area then is\nA = r^2[theta - sin(theta)]/2\n= (12)^2[1.97 - sin(1.97)]/2\n= 75.5 m^2\n\nEDIT:  My answer is indeed correct.  greatindiangenius's angle below is wrong.  You can find that angle theta another way besides the way listed on the link below - if you imagine a triangle formed by the chord and two radii, and if you drop a height from the center to the chord, then you have two triangles with long leg 10 and hypotenuse 12.  The angle between the height and the radius is arcsin(10/12) = 56.44, so the entire angle is 112.88 degrees, or 1.97 radians, not 100.\n\nRecall that a _sector_ is the pie wedge shape of a circle, starting from the center.  But a _segment_ is only the part between the chord and the circle - the ice cream part of the cone, if you break the _sector_ down like that.  So the formula in my reference and my work is correct in that we are finding the area of the ice cream only, and not the ice cream and cone.\n\nWe can find the area of the segment another way: we can take the area of the sector and subtract the are of the triangle formed by the radii and chord.\n\nFor the area of the _sector_, recall that it's just a fraction of the entire area, based on that angle 112.88:\n\nArea of sector = (112.88/360)(pi*12^2)\n= 141.85 m^2\n\nFor the area of the triangle, we need the height (we already have the base, 20).  We can use the Pythagorean theorem:\n\nc^2 = a^2 + b^2\n12^2 = 10^2 + b^2\n144 = 100 + b^2\nb^2 = 44\nb = 2sqrt(11)\n~ 6.63 m\n\nArea of triangle = (1/2)bh\n= (1/2)(20)(6.63)\n= 66.3 m^2\n\nArea of segment = Area of sector - Area of triangle\n= 141.85 - 66.3\n= 75.5 m^2\n\nwhich is the same thing as above with the other formula.
741778
This is not tricky at all. The volume is 1-1/2 cylinders of "height" 50,000 meters and radius 4 meters.\n\nThe formula for the volume of a cylinder is\n\nV = pi * r^2 * h
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I am assuming you mean something like a round flower pot, where the base is smaller than the top.  You are saying the bottom has a diameter of 17 inches and the top has a diameter of 34 inches, with a height of 34 inches (not the slant).\n\nIs this correct?  I've also heard this called a truncated cone.  The formulas for volume is given below:\n\nHeight: h\nRadius of bases: r, R\nVolume: V\n\nV = Pi(R^2+rR+r^2)h/3\n\nSo plugging in your values (don't forget to cut the diameters in half to get radii):\n\nh = 34\nr = 8.5\nR = 17\n\nV = Pi(17^2+(8.5)(17)+8.5^2) 34 / 3\nV = Pi(289 + 144.5 + 72.25) 34/3\nV = Pi(505.75)34/3\nV = Pi(505.74)(10.333)\nV = Pi(5731.833)\nV = 18007 cubic inches
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291.13 L is the correct volume.\n\nCheck your algebra when you are solving for V1.
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The volume of a cylinder equals the (area of the base)*height = π r2h
722985
For bigger cone the volume is given by V=(pi*R^2*H) and that for the smaller cone is given by v=(pi*r^2*h) where R(or r) and H(or h) represent the radius and height of the cone respectively. Therefore, V/v=(R^2*H)/(r^2*h). Now as the cones are similar so R/r=H/h=k (say). So V/v=k^3=27/8 or k=3/2 i.e. the ratio of radius of the cones is 3:2 (Ans: a). The ratio of their circular areas is A/a=(pi*R^2)/(pi*r^2)=k^2=9/4 or 9:4 (Ans: b).
22565
Step 1 is to find the volume of each of the individual spheres using formula (4/3)*pi*r^3\nSphere A diameter 2 cm\nSphere B diameter 3 cm\nsphere c diameter 4 cm\n\nSphere A Volume =(4/3)*pi*(1 cm)^3= approx 4.189 cm^3\nSphere B Volume =(4/3)*pi*(1.5 cm)^3= approx 14.137 cm^3\nSphere C Volume =(4/3)*pi*(2 cm)^3= approx 33.510 cm^3\n\nadd them together to get a volume of 51.836\n\nnow to find radius of new sphere.\n\n51.836=(4/3)*pi*r^3\n(51.836)*(3/4pi)=r^3\n12.375=r^3\nr=approx 2.313\n\ntherefore the diameter of the new sphere is about 4.626 cm
368234
The definition of the volume of an object is just how much space it occupies.\nIf you're looking for the formula for volume, then \nV = Pi(r^2)h, where r is the radius and h is the height.
433476
the volume of a trapezoid-shaped box is the height of the box times the area of the trapezoid.\nwhere H is the height of the box, and h is the height of the trapezoid with bases b and B,\nV=1/2*(b+B)*h*H
648945
What you wrote isn't a cone. It is the part of the hyperboloid of one sheet x^2+y^2-z^2=1 with z>=0. The intersection with the sphere is a circle on the sphere and so the volume is 0.\n\nIf you *meant* the cone z=sqrt(x^2+y^2), you can evaluate the volume in several ways. I would suggest changing to spherical coordinates, where the equation of both the cone and the sphere are very simple. [rho=1 and phi=pi/4] Don't forget the rho^2 sin(phi) term when integrating!
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Volume Formulas \nNote: "ab" means "a" multiplied by "b". "a2" means "a squared", which is the same as "a" times "a". "b3" means "b cubed", which is the same as "b" times "b" times "b".\nBe careful!! Units count. Use the same units for all measurements. Examples\ncube = a 3  \n\nrectangular prism = a b c  \n\nirregular prism = b h  \n\ncylinder = b h = pi r 2 h  \n\npyramid = (1/3) b h  \n\ncone = (1/3) b h = 1/3 pi r 2 h  \n\nsphere = (4/3) pi r 3  \n\nellipsoid = (4/3) pi r1 r2 r3  \n\n  \n\n  Units \n\nVolume is measured in "cubic" units. The volume of a figure is the number of cubes required to fill it completely, like blocks in a box. \n\nVolume of a cube = side times side times side. Since each side of a square is the same, it can simply be the length of one side cubed. \n\nIf a square has one side of 4 inches, the volume would be 4 inches times 4 inches times 4 inches, or 64 cubic inches. (Cubic inches can also be written in3.) \n\nBe sure to use the same units for all measurements. You cannot multiply feet times inches times yards, it doesn't make a perfectly cubed measurement. \n\nThe volume of a rectangular prism is the length on the side times the width times the height. If the width is 4 inches, the length is 1 foot and the height is 3 feet, what is the volume?\n\nNOT CORRECT .... 4 times 1 times 3 = 12 \n\nCORRECT.... 4 inches is the same as 1/3 feet. Volume is 1/3 feet times 1 foot times 3 feet = 1 cubic foot (or 1 cu. ft., or 1 ft3).
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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.