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

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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 du221a(32+32+32 )u221a(3*32 )3u221a3, and then divide the result by 2 to find the radius of the sphere, (3u221a3)/2.

What is the area of the surface of a sphere inscribed in a cube?

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.

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Can a sphere fit in a cube?

A sphere that just fits into a cubic box takes up only about 50% of the volume of the box (actually, just slightly more than half, since (1/6) 0.524)!

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

The total surface area (in sq. cm) of the cube is. Correct answer is ‘512′.

What is the surface area of a cube inscribed in a sphere with a radius of 8?

Since the edge of the cube is 12cm, the max. diameter of the sphere that can be carved out would be 12cm.

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

The total surface area (in sq. cm) of the cube is. Correct answer is ‘512′.

What is the total surface area of a cube that is inscribed in a sphere of radius 8 cm?

The total surface area (in sq. cm) of the cube is. Correct answer is ‘512’.

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

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 .

How many spheres can you fit in a cube?

In a cube of 2x2x2 cm cube, we can fit one sphere. There are ( 20 x 20 x 20) / ( 2 x 2 x2) 1000 cubes or spheres. Diameter of the sphere is 2 cm. In 20 cm side we can place 10 spheres .

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What percentage of a sphere fits in a cube?

A sphere that just fits into a cubic box takes up only about 50% of the volume of the box (actually, just slightly more than half, since (1/6) 0.524)!

How do you determine if a sphere is inside a cube?

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 u03c0 .

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

Let a be the length of side of largest cube inscribed in a sphere of diameter=2. a√3=2 ==>a=2/√3(diagonal of cube=diameter of sphere). Hence volume of cube=a^3=8/3√3.

What is cube inscribed in a sphere?

The total surface area (in sq. cm) of the cube is. Correct answer is ‘512′.

What will be the ratio of volume of cube is to volume of sphere inscribed in the cube?

If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6 : π.

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

The total surface area (in sq. cm) of the cube is. Correct answer is ‘512′.

What is the surface area of a cube in which each face of the cube has an area of surface area?

The surface area of a cube = 6a2 where a is the length of the side of each edge of the cube. Put another way, since all sides of a cube are equal, a is just the lenght of one side of a cube. We have 96 = 6a2 → a2 = 16, so that’s the area of one face of the cube.

6a2

How do you find the volume of a sphere inside a cube?

Correct answer: To find the diagonal length of the cube, we use the distance formula du221a(32+32+32 )u221a(3*32 )3u221a3, and then divide the result by 2 to find the radius of the sphere, (3u221a3)/2.

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How many spheres fit in a square?

After finding right packing, you can calculate exact value. Well, assuming each ball occupies ~1 cm 3 of space, you have fit in 1,000,000 balls just by having them in a square lattice.

What is the ratio of cubes to spheres?

So for a cube, the ratio of surface area to volume is given by the ratio of these equations: S/V 6/L. For a sphere, surface area is S 4*Pi*R*R, where R is the radius of the sphere and Pi is 3.1415 The volume of a sphere is V 4*Pi*R*R*R/3.

How many balls can fit in a box calculator?

Divide each dimension of the box by the diameter, rounding down to the next lower integer as needed. That gives you how many balls you can place side by side along the length and width, and how many you can stack vertically along the height. Then multiply the 3 integer ratios to get the number that fit in the box.

What percentage of a cube does a sphere take up?

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 d3, where d is the diameter of the sphere and also the length of a side of the cube and π6 ≈ 0.5236.
Symmetry group: O(3)
Surface area: 4πr2

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 u03c0 .

How many spheres can fit in a cuboid?

In total, the first layer will have 11 rows, for a total for cm 19.32 cm. So the bottom layer fits 105 spheres. Let us first fill the bottom layer.