Space diagonal - practice problems - page 3 of 6
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 114
- 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. - Dimensions - crate
A wooden crate with dimensions d=3m, e=4m, and f=3m was placed in a transport container with dimensions a=10 m, b=4m, and c=3m. What is the maximum length of a straight, rigid rod of negligible diameter that can still be placed in the container in this si - Nice prism
Calculate the cuboid's surface if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm. - Calculate 6214
The cube A B C D A'B'C'D 'has a section area ACC'A' equal to 64 square root of 2 cm². Calculate the surface of the cube. - Sphere and cone
Within the sphere of radius G = 33 cm, inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone? - Measures 2535
Peter wants to hide a 60 cm long whistle in a shoebox that measures 25 cm x 48 cm x 21 cm. Will he make it? - Tetrahedral pyramid
It is given a regular tetrahedral pyramid with a base edge of 6 cm and a height of pyramid 10 cm. Calculate the length of its side edges.
- Cube in sphere
The cube is inscribed in a sphere with a radius r = 6 cm. What percentage is the cube's volume from the ball's volume? - 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? - Solid cuboid
A solid cuboid has a volume of 40 cm³. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig. - Body diagonal
Cuboid with base 7cm x 3,9cm and body diagonal 9cm long. Find the height of the cuboid and the length of the diagonal of the base, - Cube diagonals
The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal. - Cube wall
The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube. - 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). - 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.
- Centimeters 5533
Calculate the area of one cube wall and the wall diagonal of a cube if its volume equals 1728 cubic centimeters. - Cube diagonals Calculate the length of the side and the diagonals of the cube with a volume of 27 cm³.
- 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 - Calculate 2674
Calculate the volume of the block if a = 3 cm, the size of the body diagonal is 10 cm and the size of the diagonal of the base is 5 cm - 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 .
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