Space diagonal + sphere - practice problems
Number of problems found: 15
- Sphere area
A cube with an edge 1 m long is a circumscribed sphere (vertices of the cube lie on a sphere's surface). Find the surface area of the sphere. - Cube into sphere
The cube has brushed a sphere as large as possible. Determine how much percent the waste was. - Cube in ball
The cube is inscribed into the sphere of radius 6 dm. How many percent is the volume of the cube of the volume of the sphere? - Billiard balls
A layer of ivory billiard balls radius of 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to everyone adjacent to it. In the spaces between sets of 4 adjacent balls, other balls rest, equal in size to the original. - Cubes
A sphere is inscribed in one cube and the same sphere is circumscribed about another cube. Calculate the difference between the volumes of the two cubes if the difference between their surface areas is 231 cm². - Cube in a sphere
A cube is inscribed in a sphere with volume 8101 cm³. Determine the edge length of the cube. - Two balls
Two balls, one 8 cm in radius and the other 6 cm in radius, are placed in a cylindrical plastic container 10 cm in radius. Find the volume of water necessary to cover them. - 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 the corner of a room. The spheres are each tangent to the walls and floor an - Sphere cube filling
Nine identical spheres are stacked in the cube to fill the cube's volume as much as possible. What part of the volume will the cube fill? - Cube in sphere
The cube is inscribed in a sphere with a radius r = 6 cm. What percentage is the cube's volume from the ball's volume? - Sphere vs cube
How much % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere? - Sphere and cone
Within the sphere of radius G = 33 cm, inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone? - Inscribed cube
A cube is inscribed in a sphere with a radius of 27 cm. Calculate its volume and surface area. - Cube and sphere
A cube with a surface area of 150 cm² is inscribed in a sphere. What is the surface area of the sphere? - Cube in sphere
The sphere is an inscribed cube with an edge of 8 cm. Find the sphere's radius.
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