How do you find the volume of a sphere inscribed in a cube?
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How do you find the volume of a sphere inscribed in a cube?
If s is the side length of the cube, we have that Vcube=s3. Notice that the largest possible sphere that can fit inside the cube is the inscribed sphere, which has radius 12s. Using the volume formula for a sphere, we find that Vsphere=43πr3=43πs38=π6s3.
How do you find the radius of a sphere inscribed in a cube?
Correct answer: To find the diagonal length of the cube, we use the distance formula d=√(32+32+32 )=√(3*32 )=3√3, and then divide the result by 2 to find the radius of the sphere, (3√3)/2.
How do you find the surface area of a cube of a sphere?
Correct answer: The side of the cube is the same as the diameter of the sphere. Since d = 4, r = 2. The surface area of a sphere is found by SA = 4π(r2) = 4π(22) = 16π.
What is cube inscribed in a sphere?
When a cube is inscribed in a sphere, the long diagonal of the cube is a diameter of the sphere. Since the sphere has a radius of 6 and a diameter of 12, you know that the sphere has a long diagonal of 12. The long diagonal of a cube is related to a side of the cube using the formula d = s .
What is cube and sphere?
is that cube is (geometry) a regular polyhedron having six identical square faces while sphere is (geometry) the set of all points in three-dimensional euclidean space (or n -dimensional space, in topology) that are a fixed distance from a fixed point.
What is the surface area of a cube inscribed in a sphere with a radius of 8 as shown above?
The total surface area (in sq. cm) of the cube is. Correct answer is ‘512’.
What is cube length?
Since the volume of a cube is length times width times height, with every measurement being the same, we just need to take the cube root of the volume: Rounded to the nearest tenth, the length is 3.5 feet.
What is volume of the sphere?
The formula for the volume of a sphere is V = 4/3 πr³.
How much of a cube is a sphere?
Interested in language and maths (particularly solid geometry) and … Volume of cube = a^3, where a is the length of the cube edge. The sphere that fits in the cube has radius a/2. Volume of a sphere radius r is (4.
What will be the ratio of volume of cube is to volume of sphere inscribed in the cube?
6:π
If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be6:π.
What is the cube formula?
| Sr.No | Cube | Cuboid |
|---|---|---|
| 9 | Diagonal = √3 × (edge) | Diagonal = √(l² + b² + h²) where, l = length, b = breadth and h = height |
| 10 | Volume = (edge)³ | Volume = l × b × h where,l = length, b = breadth and h = height |
| 11 | Perimeter = 12 (edge) | Perimeter = 4(l + b+ h) where, l = length, b = breadth and h = height |