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A sphere segment is cut off from a sphere k with radius r = 1. The volume of the sphere inscribed in this segment is equal to 1/6 of the volume of the segment. What is the distance of the cutting plane from the center of the sphere?

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I have noticed that your integration limits are not correct (cylindrical ones). Take into account that the radius goes from zero to r, but not R (since the radius of the cap (r) is not the same that the radious of the sphere (R)). JavaScript exercises, practice and solution: Write a JavaScript program to calculate the volume of a sphere.

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double radius = 0; double volume = 0; double area = 0; System.out.print("Radius of Sphere: "); radius = input.nextDouble() Formula for calculating the volume of a sphere.We now have the volume of a sphere of known diameter r . Since d is the normal representation for diameter, we can restate the volume formula in terms of both the diameter d and radius r recognizing that d = 2r: Vsphere = 1 6 d3 or Vsphere = 1 6 2r 3= 4 3 r3

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Python: Volume of a Sphere. A sphere is a three-dimensional solid with no face, no edge, no base and no vertex. It is a round body with all points on its surface equidistant from the center. pi = 3.1415926535897931 r= 6.0 V= 4.0/3.0*pi* r**3 print('The volume of the sphere is: ',V).

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Another approach to obtaining the formula comes from the fact that it equals the derivative of the formula for the volume with respect to r because the total volume inside a sphere of radius r can be thought of as the summation of the surface area of an infinite number of spherical shells of infinitesimal thickness concentrically stacked inside ...

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sphere surface area = 4 * pi * r³. sphere volume = 4⁄3 (pi * r³) Step 2: Determine the Inputs and Outputs. As stated at the beginning of this article, the user will input the radius of a circle or sphere, and the calculator will return the area and circumference (if a circle) or the surface area and volume (if a sphere). Develop a program in C to find the volume of the sphere using the following formula: volume of the sphere = pi • radius; where pi is the constant value 3.14. Develop a program in C to find the biggest of 3 numbers using else-if statement.

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The volume of a cylinder with radius r and height 2r would be 2πr 3 (2r * base area of πr 2) The sphere which fits snugly into that cylinder has radius r and a volume 2/3 that of the cylinder, for (4/3)πr 3. As for why the sphere has a volume 2/3 that of the cylinder, I don't have a simple explanation.

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Processing... ... ... Calculates volume of geometric shapes: cube, prism, pyramid, frustum, cone, cylinder, sphere, ellipsoid. person_outline Anton schedule 2008-11-19 18:42:11 This article contains a collection of calculators for calculating geometric figures volume.

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Dec 10, 2016 · Working 2,000 years before the development of calculus, the Greek mathematician Archimedes worked out a simple formula for the volume of a sphere: Of his many mathematical contributions, Archimedes… Volume of a Sphere equals 4/3 x πr^3 In this example our radius is 6 and six squared is 36 and 36 times 4 is 144 π units squared. Now to find the volume use 3 as the radius so 3 cubed is 27 and 27 times 4⁄3 is 36π units cubed so those are the two formulas for volume and surface area of a cube.

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Theorem: The volume of a sphere of radius r is given by the formula: VSPHERE = 3 4 π r 3 Proof: We first establish the equality of the volume of the bowl shaped region bounded beneath a cone inscribed in a circular cylinder having height r and base radius r with that of the hemisphere of radius r.

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