Space diagonal - practice problems - page 2 of 6
Remember: Solve each problem thoughtfully and make sure to show your complete solution for every question.Number of problems found: 114
- Regular 4BH
A regular quadrilateral prism has a volume of 864 cm³ and the area of its surface is twice the area of its base. Determine the size of its body 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 . - Quadrilateral prism
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. - 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. - Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in the corner of a room. The spheres are each tangent to the walls and floor an - 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 - Cuboid face diagonals
The lengths of the cuboid edges are in the ratio 1:2:3. Will the lengths of its diagonals be in the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid. - 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 - 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. - 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. - Totem shed fitting
The boys wanted to store their hand-made totem 5.1 m high in the block-shaped shed, which measures 4 m, 3 m, and 2 m, for the winter. Will it fit in there at all? - Longest rod
The toolbox has internal dimensions, a length of 1.5 meters, a width of 80 cm, and a height of 6 dm. Calculate the longest rod we can hide in this box. - Suitcase - rod
The trunk of a car has the shape of a cuboid with sides 1.6m x 1.2m x 0.5m (width, depth, height). Determine the longest thin rod that can be placed on the bottom. - Ratio of edges
The cuboid dimensions are in a ratio of 3:1:2. The body diagonal has a length of 28 cm. Find the volume of a cuboid. - Cuboid - volume, diagonals
The length of the one base edge of cuboid a is 3 cm. The body diagonal is ut=13 cm, and the diagonal of the cuboid's base is u1=5 cm. What is the volume of the cuboid? - Cuboid
Cuboid with edge a=6 cm and space diagonal u=31 cm has volume V=900 cm³. Calculate the length of the other edges. - Diagonal
Determine the dimensions of the cuboid if it is diagonally long 60 dm and has an angle with one edge 35° and with another edge 77°. - Sphere cube filling
Nine identical spheres are stacked in the cube to fill the cube's volume as much as possible. What part of the volume will the cube fill? - Box volume
Calculate the volume of a wooden box in the shape of a prism with the base of a rectangle if the box's width is 8 dm, the length is 14 dm, and the size of the body diagonal is 25 dm. - Cube in a sphere
The cube is inscribed in a sphere with a volume 8101 cm³. Determine the length of the edges of a cube.
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