# Sphere + space diagonal - problems

1. Cube in a sphere
The cube is inscribed in a sphere with volume 6116 cm3. Determine the length of the edges of a cube.
2. Cube in ball
Cube is inscribed into sphere of radius 241 cm. How many percent is the volume of cube of the volume of sphere?
3. Two balls
Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
4. Sphere and cone
Within the sphere of radius G = 33 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
5. Sphere area
A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere.
6. Sphere vs cube
How many % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere?
7. Cube and sphere
Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
8. Billiard balls
A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original. T
9. Cube in sphere
The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
10. Cube into sphere
The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
11. Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor and

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