Space diagonal of Cuboid Problems
Number of problems found: 60
- Cuboid - sum of edges length
Calculate the cuboid's dimensions if the sum of its edges is 19 cm. The body's diagonal size is 13 cm, and its volume is 144 cm³. The total surface area is 192 cm². - Volume and body diagonal
Calculate how much the cuboid's volume and body diagonal decrease if we reduce each of its three edges, a, b, and c, by 18%. - Boxes
Petra has planted flowers in two boxes in the shape of a cube. The first box has an internal dimension of 70 cm and the second 5 dm. She wants to make one box in the shape of a cuboid, into which she could transplant both flowers from these boxes. The new - Faces diagonals
Find the cuboid volume if the cuboid's diagonals are x, y, and z (wall diagonals or three faces). Solve for x=1.6, y=1.8, z=1.6 - 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°. - Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and whose body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, and c have dimensions in the ratio of 10:8:9. If you know that the diagonal wall AC is 75 cm, and the angle between AC and space diagonal AG is 30 degrees. - Forces
At point G, three mutually perpendicular forces act: F₁ = 16 N, F₂ = 7 N, and F₃ = 6 N. Determine the resultant force F and the angles between F and each of F₁, F₂, and F₃. - Calculate cuboid, diagonals
The volume of a cuboid with a square base is 64 cm3, and the space diagonal deviation from the base's plane is 45 degrees. Calculate its surface area. - 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). - Quadrilateral prism
Calculate the volume and surface area of a regular quadrilateral prism with base edge a=24 cm if the space diagonal makes an angle of 66° with the base. - Dimensions - crate
A wooden crate with dimensions d=3 m, e=4 m, and f=3 m was placed in a transport container with dimensions a=10 m, b=4 m, and c=3 m. What is the maximum length of a straight, rigid rod of negligible diameter that can still be placed in the container in th - 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. - Prism and wall diagonal
The ABCDA'B'C'D' prism has a square base. The wall diagonal of the AC base is 9.9 cm long, and the body diagonal AC' is 11.4 cm long. Calculate the surface area and volume of the prism. - Regular 4BH A regular quadrilateral prism has a volume of 864 cm³ and its total surface area is twice the area of its base. Determine the length of its space diagonal.
- 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 . - 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 - Right triangular prism
We have a cuboid with a base and dimensions of 12 cm and 5 cm and a height of 4 cm. The tablecloth is cut into two identical triangular prisms with right triangular bases. We painted the surface of the created prisms with color. Calculate the surface area - Regular square prism
The volume of a regular square prism is 192 cm³. The size of its base edge and the body height is 1:3. Calculate the surface of the prism. - 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.
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