Diagonal + angle - practice problems - last page
Number of problems found: 118
- Pyramid - angles
In a regular pyramid in which the edge of the base is | AB | = 4 cm; height = 6 cm, calculate the angle of the lines AV and CV, V = vertex. - Quadrilateral prism
The body diagonal of a regular quadrilateral prism forms an angle of 60° with the base. The edge of the base is 20 cm long. Calculate the volume of the body. - Calculate cuboid
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 . - Base diagonal
In a regular four-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the pyramid's surface area and volume. - Deviation of the lines
Find the deviation of the lines AG BH in the ABCDEFGH box-cuboid if given | AB | = 3 cm, | AD | = 2 cm, | AE | = 4 cm - Space diagonal angles
Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28 cm, b = 45 cm, and c = 73 cm. Then, find the angle between the body diagonal and the plane of the base ABCD. - 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 10 cm. Calculate the body volume. - Quadrilateral pyramid
In a regular quadrilateral pyramid, the side edge is e = 7 dm, and the base's diagonal is 50 cm. Calculate the pyramid shell area. - Cuboid
Find the dimensions a, b, and c of a cuboid whose space diagonal is d = 6 dm and makes an angle α = 35° with edge a and an angle β = 66° with edge b. - Quadrilateral pyramid The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base
- Diagonal
Determine the dimensions of a cuboid whose space diagonal is 60 dm and makes an angle of 35° with one edge and 77° with another edge. - Side edges
The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid. - Pyramid Side Edge Length
If the pyramid's height is 4 cm and the base area is 16 cm2, include the side edge length of a regular quadrilateral pyramid. - Square pyramid
Calculate the pyramid's volume with the side 5 cm long and with a square base, and the side base has an angle of 60 degrees. - 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? - Cube - angles
Calculate the angle alpha (α) between the face diagonal and the base of a cube. Calculate the angle beta (β) between the space diagonal and the base of the cube. - Box
Calculate the angle between the base of a cuboid with dimensions 5 × 10 and its space diagonal of length 13. - Angle of the body diagonals
Using the vector dot product calculate the angle of the body diagonals of the cube.
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