What is volume of cube inside sphere?

What is volume of cube inside sphere?

volume of the cube is X3. volume of the sphere is 4/3×π×radius3. area of cube is 6X2. area of sphere is 4×π×radius2.

How do you find the volume of a cube inscribed in a sphere?

If we let the edge length of the cube be a, then the largest diagonal of the cube will be equal to a√3 by the Pythagorean Theorem, and this will also be the diameter. From the formula for the volume of a sphere given the diameter (16πd3), the area of the sphere is equal to π6×(a√32)3=πa3√316.

What is the maximum possible volume of a sphere that can fit inside a cube of side 6 cm?

So, for the largest sphere in a cube, the diameter of the sphere will be equal to side of the cube. Therefore, the volume of the largest sphere inside the given cube is 36 π .

What is the volume of a box that can be inscribed in a sphere of unit radius?

The maximal volume of the rectangle inside the sphere of radius r and that volume is 8r3/3√3.

Does a cube have maximum volume?

a) The volume will be a maximum when a cube is used. The side length of the required cube is 6.3 cm.

Are cubes inside spheres?

Explanation: We know that the cube has a volume of 27 cubic inches, so each side of the cube must be ∛27=3 inches. Since the cube is inscribed inside the sphere, the diameter of the sphere is the diagonal length of the cube, so the radius of the sphere is half of the diagonal length of the cube.

What is the radius of the largest possible sphere that can be inscribed in a cube of edge 6 cm?

The radius is r= 3 cm.

How many spheres fit inside a rectangular prism?

The upshot is: 540 balls (twelve layers of 45 in the hexagonal close-packing) just fit into a box with the given dimensions.

What is the volume of this sphere?

Volume of a sphere: V = (4/3)πr.

Does a cube or cylinder have more volume?

A cylinder is described by two measurements, its height ℎ and its base radius 𝑟. Its volume is given by 𝜋𝑟 squared ℎ. Here, 𝜋𝑟 squared gives the area of the circular base. So we can see that the volume of the cylinder will be larger than the volume of the cube.

What is the sphere inside a cube?

For most practical purposes, the volume inside a sphere inscribed in a cube can be approximated as 52.4% of the volume of the cube, since V = π6 d 3, where d is the diameter of the sphere and also the length of a side of the cube and π6 ≈ 0.5236.

How do you calculate a sphere?

Sphere size is calculated using two measures: the volume (how much space the sphere takes up) and the surface area (the total area of the sphere’s surface). Both sphere size and surface area can be easily calculated if you know the radius or diameter of the sphere. The formula for volume is 4/3 times pi times the radius cubed, or 4/3πr^3.

What is the formula for the diameter of a sphere?

Derivation of the above radius of a sphere formulas is, in fact, straightforward. You need to make some algebraic transformations using the following basic equations: Diameter of a sphere: d = 2 * r, Surface area of a sphere: A = 4 * π * r², Volume of a sphere: V = 4/3 * π * r³,