# Body diagonal - examples

- 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. - Cube in a sphere

The cube is inscribed in a sphere with volume 6598 cm^{3.}Determine the length of the edges of a cube. - Cuboid

Cuboid with edge a=14 cm and body diagonal u=42 cm has volume V=10976 cm^{3.}Calculate the length of the other edges. - Cube diagonal

Determine length of the cube diagonal with edge 55 dm. - Forces

In point X acts three orthogonal forces: F_{1}= 13 N, F_{2}= 8 N and F_{3}= 15 N. Determine the resultant of F and the angles between F and forces F_{1}, F_{2}and F_{3}. - 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. - Diagonal

Determine the dimensions of the cuboid, if diagonal long 16 dm has angle with one edge 66° and with other edge 71°. - 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? - Prism

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? - Vector

Calculate length of the vector v⃗ = (-2.5, 6.25, -4.25). - 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? - Box

Calculate the angle between box base 5 x 7 and body diagonal length 14. - 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. - Cuboid

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). - Trunk

Calculate length of the biggest fishing rod can be inserted into the trunk of a car with dimensions 162 x 70 × 59 cm? - Nice prism

Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm. - 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? - 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 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 - 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?

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