Body diagonal - examples
- Cube in sphere
The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
- Cube diagonal
Determine length of the cube diagonal with edge 55 dm.
The lenght, width and height of a right prism are 18, 14 and 9 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees).
- Cube in ball
Cube is inscribed into sphere of radius 136 mm. How many percent is the volume of cube of the volume of sphere?
- Cube in a sphere
The cube is inscribed in a sphere with volume 6598 cm3. Determine the length of the edges of a cube.
Calculate length of the biggest fishing rod can be inserted into the trunk of a car with dimensions 162 x 70 × 59 cm?
Cuboid with edge a=14 cm and body diagonal u=42 cm has volume V=10976 cm3. Calculate the length of the other edges.
- 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?
Calculate length of the vector v⃗ = (-2.5, 6.25, -4.25).
- Body diagonal
Find the cube surface if its body diagonal has a size of 6 cm.
Calculate the angle between box base 5 x 7 and body diagonal length 14.
- 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.
- 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.
- Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 7:10:8 and if you know that the wall diagonal AC is 21 cm and angle between AC and the body diagonal AG is 40 degrees.
- Tetrahedral pyramid
It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
Determine the dimensions of the cuboid, if diagonal long 16 dm has angle with one edge 66° and with other edge 71°.
- 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.
- Cube and sphere
Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
- 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