Sphere + space diagonal - problems

  1. Cube in a sphere
    cube_in_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
    sphere2 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
    balls-inside-cylinder 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
    cone_in_sphere 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
    sphere 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
    koule_krychle 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
    gule_1 Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
  8. Billiard balls
    balls_billiard 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
    sphere4 The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
  10. Cube into sphere
    cube_sphere_in The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
  11. Tangent spheres
    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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