Angle + space diagonal - practice problems
Number of problems found: 18
- Cuboid
Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine the angle between the body diagonal and the base plane (round to degrees). - Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and the body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - Deviation of the lines
Find the deviation of the lines AG BH in the ABCDEFGH box-cuboid if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm - Space diagonal angles
Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm, and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD. - Angle of the body diagonals
Using the vector dot product calculate the angle of the body diagonals of the cube. - Box
Calculate the angle between box base 9 x 14 and body diagonal length 18. - Four sided prism
Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm, and the diagonal body forms a 50-degree angle with the base plane. - Prism diagonal
The body diagonal of a regular square prism has an angle of 60 degrees with the base, and the edge length is 10 cm. What is the volume of the prism? - Diagonal
Determine the dimensions of the cuboid if diagonal long 60 dm has an angle with one edge 35° and with another edge 77°. - Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, and c has dimensions in the ratio of 7:8:10. If you know that the diagonal wall AC is 56 cm, and the angle between AC and space diagonal AG is 25 degrees. - Calculate 82567
The volume of a cuboid with a square base is 64 cm3, and the body diagonal deviation from the base's plane is 45 degrees. Calculate its surface area. - Distance of points
A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S. - Quadrilateral prism
The height of a regular quadrilateral prism is v = 10 cm, and the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the prism's volume. - Quadrilateral prism
Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°. - Calculate 82992
Given cuboid ABCDEFGH. We know that |AB| = 1 cm, |BC| = 2 cm, |AE| = 3 cm. Calculate in degrees the angle size formed by the lines BG and FH . - Diagonals of a prism
The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal and the base's diagonal. - Angle of diagonal
The 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. - Quadrilateral 82146
Calculate the volume and surface area of a regular quadrilateral prism with base edge a=24 cm if the body diagonal makes an angle of 66° with the base.
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