Body volume + 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. Cuboid Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
3. 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?
4. 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.
5. Cube wall Calculate the cube's diagonal diagonal if you know that the surface of one wall is equal to 36 centimeters square. Please also calculate its volume.
6. Cuboid - volume, diagonals The length of the one base edge of cuboid a is 3 cm. Body diagonal is ut=13 cm and diagonal of cuboid's baseis u1=5 cm. What is the volume of the cuboid?
7. Concrete block Determine the volume of concrete block whose one edge of the base has a length 3 meters, body diagonal is 13 meters and its height is 12 meters.
8. Cube diagonals Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
9. Four sided prism Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
10. Solid cuboid A solid cuboid has a volume of 40 cm3. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has length 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.
11. Ratio of edges The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
12. Angle of diagonal Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
13. Volume and body diagonal Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%?
14. Cube into sphere The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
15. Body diagonal Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
16. Body diagonal - cube Calculate the surface and cube volume with body diagonal 15 cm long.
17. Prism diagonal The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
18. Body diagonal Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
19. Cube diagonals Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.

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