# Body diagonal + Pythagorean theorem - examples

- Cube in a sphere

The cube is inscribed in a sphere with volume 1587 cm^{3}. Determine the length of the edges of a cube. - Cuboid

Cuboid with edge a=6 cm and body diagonal u=35 cm has volume V=1980 cm^{3}. Calculate the length of the other edges. - Cube diagonal

Determine length of the cube diagonal with edge 33 km. - Forces

In point O acts three orthogonal forces: F_{1}= 20 N, F_{2}= 7 N and F_{3}= 19 N. Determine the resultant of F and the angles between F and forces F_{1}, F_{2}and F_{3}. - Diagonal

Determine the dimensions of the cuboid, if diagonal long 31 dm has angle with one edge 61° and with other edge 52°. - Prism

The lenght, width and height of a right prism are 6, 17 and 10 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism? - 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. - Vector

Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2). - Sphere and cone

Within the sphere of radius G = 36 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 9 x 14 and body diagonal length 18. - 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). - 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. - 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. - 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? - Body diagonal

Cuboid with base 7cm x 3,9cm and body diagonal 9cm long. Find the height of the cuboid and the length of the diagonal of the base, - 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? - Cube wall

The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube. - 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. - Cube diagonals

Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.

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Pythagorean theorem is the base for the right triangle calculator.