A number's cube root is another number that can be multiplied together three times to make the original number. X is the value that we are determining the cube root of.Substitute the formula for finding the radius of a sphere that circumscribes a cube for the radius term in the formula for the volume of a sphere. Circumscribed Sphere Volumeįree Circumscribed Sphere Volume Calculator V = (4/3)π(S * √3/2) 3 This formula substitutes the formula for finding the radius of a sphere tangent to the edge of a cube for the radius term in the formula for finding the volume of a sphere. Sphere Volume Tangent to Cube Edgesįree Volume of a Sphere Tangent to Cube Edge Calculator V = (4/3)π(S/√2) 3 To complete the formula substitute the radius R with our method for finding the radius of an inscribed sphere. The volume of a sphere can be found using the formula V = (4/3)π R 3. Previously we found the formula for the radius of an inscribed sphere, recall it was R = S/2. π (Pi) is a mathematical constant defined by the ratio of the circumference of a circle to the diameter of a circleĪn inscribed sphere is completely contained by a cube touching only its faces.V is the volume of a sphere inscribed in a cube.R is the radius of a sphere that circumscribes a cubeĪ sphere that completely contains a cube and touches each of its vertices is said to circumscribed the cube.įree Inscribed Sphere Radius Calculator V = (4/3)π(S/2) 3.Circumscribed Sphere Radiusįree Circumscribed Sphere Radius Calculator R = S * √3/2 This sphere will poke through the faces of the cube but not be large enough to enclose the entire cube as the cube corners will poke out of the sphere. R is the radius of a sphere tangent to the edges of a cubeĪ sphere that touches the edges of a cube only once on every side of the cube is said to be tangent to the edges of the cube.Sphere Radius Tangent to Cube Edgesįree Radius of a Sphere Tangent to Cube Edge Calculator R = S/√2 Therefore, the largest sphere that can be inscribed in a cube is tangential to the faces of the cube (it doesn't stick through the cube anywhere, it is totally inside the cube). In mathematics the term tangent is used to refer to two entities that touch in one place without crossing.
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