Body diagonal - examples
- Cube and sphere
Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
- Cube diagonal
Determine length of the cube diagonal with edge 91 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).
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.
- 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.
- 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.
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.
- 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
- 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.
- 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?
- Sphere and cone
Within the sphere of radius G = 26 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?