Prepare a graduated cylindrical container filled with water. The distance between those plates equals the diameter of a sphere. You can use two parallel planes and put the sphere between them. However, how can you find this center in the real, physical sphere, especially when it's closed? Let's look on a two of our suggestions: You only have to find the center of the sphere and measure the distance to any point on its surface. Surface to volume ratio of a sphere: A / V = 3 / r A / V = 3 / r A / V = 3/ r.Volume of a sphere: V = 4 / 3 × π × r 3 V = 4/3 \times π \times r^3 V = 4/3 × π × r 3 and.Surface area of a sphere: A = 4 × π × r 2 A = 4 \times π \times r^2 A = 4 × π × r 2.Diameter of a sphere: d = 2 × r d = 2\times r d = 2 × r.You need to make some algebraic transformations using the following basic equations: Check out our length conversion to learn how to switch between different units of length!ĭerivation of the above radius of sphere formulas is, in fact, straightforward. Moreover, you can freely change the units (SI and imperial units). Our radius of a sphere calculator uses all of the above equations simultaneously, so you need to enter just one chosen quantity. Given surface to volume ratio: r = 3 / ( A / V ) r = 3 / (A/V) r = 3/ ( A / V ).Given diameter: r = d / 2 r = d / 2 r = d /2,.Below, we have provided an exhaustive set of the radius of a sphere formula: How to find the radius of a sphere? Actually, there are many varied answers to that question because it depends on what we know about a specific sphere. If you want to learn more about that kind of object, check out our area of a hemisphere calculator and volume of a hemisphere calculator. The description of a hemisphere is a little bit more complicated compared to the full sphere, but it is possible. ![]() You just need to divide a sphere into two equal parts. There is an object called hemisphere that you can construct from any sphere you want. For more general information about spheres, check out our sphere calc! This radius of a sphere calculator, as the name suggests, contains information dedicated mostly to the radius of a sphere. Also, here we can find the analogy to the circle, which encloses the largest area with a given perimeter. A / V A / V A / V – Surface to volume ratio of a sphere.Ī sphere is a special object because it has the lowest surface-to-volume ratio among all other closed surfaces with a given volume.Since the area of the sphere is 4πR2, the area of a diangle of angle α must be 2αR2. Hence, the total area of the sphere can be written asĬlearly, a diangle occupies an area that is proportional to the angle it forms. Note that these diangles cover the entire sphere while overlapping only on the triangles ABC and A′B′C′. Similarly, we can form diangles with vertices on the diameters BB′ and CC′ respectively. Two diangles with vertices on the diameter AA′ are shown below.Īt each vertex, these diangles form an angle of ∠A. As its name suggests, a diangle is formed by two great arcs that intersect in two points, which must lie on a diameter. By symmetry, both triangles must have the same area.įor the proof of the above formula, the notion of a spherical diangle is helpful. The triangle A′B′C′ is antipodal to ABC since it can be obtained by reflecting the original one through the center of the sphere. Note that by continuing the sides of the original triangle into full great circles, another spherical triangle is formed. For the purposes of the above formula, we only consider triangles with each angle smaller than π.Īn illustration of a spherical triangle formed by points A, B, and C is shown below. Since the sphere is compact, there might be some ambiguity as to whether the area of the triangle or its complement is being considered. Incidentally, this formula shows that the sum of the angles of a spherical triangle must be greater than or equal to π, with equality holding in case the triangle has zero area. The area of a spherical triangle ABC on a sphere of radius R is More precisely, the angle at each vertex is measured as the angle between the tangents to the incident sides in the vertex tangent plane. The measurement of an angle of a spherical triangle is intuitively obvious, since on a small scale the surface of a sphere looks flat. A spherical triangle is formed by connecting three points on the surface of a sphere with great arcs these three points do not lie on a great circle of the sphere.
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