Space diagonal - practice problems
Space diagonal (also interior diagonal or body diagonal) of a polyhedron (i.e. prism, cube or rectangular cuboid) is a line connecting two vertices that are not on the same face. Space diagonals contrast with face diagonals, which connect vertices on the same face (but not on the same edge) as each other.Remember: Solve each problem thoughtfully and make sure to show your complete solution for every question.
Number of problems found: 118
- 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. - Sphere area
A cube with an edge 1 m long is a circumscribed sphere (vertices of the cube lie on a sphere's surface). Find the surface area of the sphere. - Cube into sphere
The cube has brushed a sphere as large as possible. Determine how much percent the waste was. - Cube in ball
The cube is inscribed into the sphere of radius 6 dm. How many percent is the volume of the cube of the volume of the sphere? - 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 - Billiard balls
A layer of ivory billiard balls radius of 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to everyone adjacent to it. In the spaces between sets of 4 adjacent balls, other balls rest, equal in size to the original. - Wire model
A wire model of a regular hexagonal prism has a base edge length of a = 8 cm and a height of v = 12 cm. The solid is covered with paper — the bases with dark paper and the lateral surface with white paper. - Calculate in cm the greatest possible straight- - Cubes
A sphere is inscribed in one cube and the same sphere is circumscribed about another cube. Calculate the difference between the volumes of the two cubes if the difference between their surface areas is 231 cm². - 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. - 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. - Four sided prism
Calculate the volume and surface area of a regular quadrilateral prism whose height is 28.6 cm, and the diagonal body forms a 50-degree angle with the base plane. - The glass
The glass has the shape of a cylinder with an inner diameter of 12 cm, and the height from the bottom is 16 cm. The cut skewer can be inserted diagonally into the glass so it does not protrude beyond the edge. What is the largest possible length of the cu - 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.
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