Hemisphere When a sphere is divided perfectally into two halves, each half is called a hemisphere. The measurement of a sphere's diameter is exactly twice its radius, and is show in the sphere calculator above as the vertical measurement labeled 'd' in the preview. Diameter A sphere's diameter is a line segment that extends from one point on the sphere's surface, through the center point and terminating on an antipodal point on the opposite side of the sphere's surface. Ball A solid shape consisting of all points within a sphere's volume. Each individual point is called an antipode. The two points that start and end the diameter are antipodal points. A sphere's diameter is a line segment that extends from one point on the surface, through the center point and to the opposite side of the sphere. Antipode Antipodes are two opposite points on a sphere's surface. Sphere A sphere is a three dimensional surface described by a single dimension, the sphere's radius, that when swept through three dimensions creates a closed surface. For surface area, you can think of the problem in terms of how many squares with height and width dimensions equal to the radius it will take to cover the surface of the sphere. These calculations for a sphere are also intricately related to π. However, unlike two dimensional shapes, three dimensional solids by definition have a surface area and a volume. The radius, diameter and circumference of that circle will be the same as that circle. An orthogonal two dimensional section through a sphere yeilds a circle, and if that section also includes the sphere's center point, the circle will be the maximum size that can be created by slicing that sphere. Like its two dimensional cousin the circle, a sphere's geometry is intertwined with the constant pi (π). A sphere is the most efficent shape in terms of its ratio of surface area to volume. The different variables relating to a sphere's geometry can be calculated from each other using a small number of formulae all related to a sphere's radius, which again is the one dimension necessary to determine a sphere's size, surface area and volume. The uniform geometry of a sphere makes it attractive when approximately a number of math and physics problems. Fundamental particles such as protons, the nucleus of a hydrogen atom, are considered to be very small spheres with a radius of roughly (0.85 × 10 -15 meters. Physicists consider spheres and the tineiest conceivable scales. And spheres are commonly used in industrial applications, for example as high-pressure fluid tanks or as components in ball bearings. Many toys you played with as a child, including balls and marbles, are spheres. The Sun, the Earth and the planets are all approximately spherical shape. While perfect mathematically perfect spheres are rare in the real world, we encounter the approximation of spherical objects of all sizes regularly. Mathematicians will sometimes distinguish between a shere and its enclosed volume by referring to the later as a ball. While a sphere encapsulates a volume, the space inside the sphere is not considered part of the sphere. Technically, a sphere is comprised only of this surface. Because of this unique symmetry, a sphere can be defined by only a single measurement, its radius, which when swept in all three dimensions describes a mathematically closed surface. What are Spheres?Ī sphere is a curved symetrical three dimensional surface, where every point on that surface is exactly the same distance from a center origin. This will also display buttons with the calculated sphere radius and volume values that can be used to copy these calculations to the clipboard.įinally, to calculate the radius and area in terms of the sphere's volume, click the 'Volume' button and enter the known volume. To calculate a sphere's radius and volume in terms of its surface area, you can click the 'Area' button and supply the known value for the area. To save either the calculated surface area or volume, click the button that shows the resulting value and it will be copied to the clipboard, or click the 'Save' button to store the calculation in the calculator tape for later reference. The surface area and volume will appear in the both the sphere preview and the math area, where the formulae used to make the calculations are shown. To compute the surface area and volume of a sphere in terms of its radius (or diameter, or circumference), click the 'Radius' button and enter the known value. This calculator allows you to compute various measurements of a sphere given a known value.
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