11/1/2022 0 Comments Formula volumen cuboX 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. R is the maximum radius of a sphere inscribed in a cubeĪ sphere that is inscribed in a cube is one that mathematically touches the face of the cube without penetrating any part of the cube.Inscribed Sphere Radiusįree Inscribed Sphere Radius Calculator R = S/2 This formula calculates the maximum length of a diagonal line running through cube volume from a vertex to another vertex that forms the opposite corner, this is the longest line that can be draw through a cube's volume. L is the maximum length of a diagonal through a cube.Volume Diagonal Lengthįree Cube Volume Diagonal Length Calculator L = √3S Since the face of a cube is a square is formula also applies to diagonals across the face of a square and is essentially a two dimensional problem. This formula calculates the length of a diagonal line running across a single cube face from a vertex to another vertex that forms the opposite corner, this is the longest line that can be draw across a cube's face. L is the length of a diagonal line across a cube's face (through a square).Face Diagonal Lengthįree Cube Face Diagonal Length Calculator L = √2S Then multiplying the area of one square (a face) by the total number of faces (six), we now know the total surface area of the cube. To find the total surface area first find the surface Area of a square by multiplying Side length by Side length, this is the same as saying Side 2. A is the surface area of the rectangular prismĪ cube is comprised of six equal squares.Surface Area of a Cubeįree Cube Surface Area Calculator A = 6S 2 However, all Length lines must run parallel to each other, as must all Width and Height lines to their respective partners.
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