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
- Diagonal 8192
Find the volume and surface of a cube if you know the length of its body diagonal u = 216 cm. - Dimensions 4700
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. - Trunk
Calculate the length of the biggest fishing rod that can be inserted into the trunk of a car with dimensions 152 x 82 × 81 cm. - Calculate cuboid, diagonals
The volume of a cuboid with a square base is 64 cm3, and the body diagonal deviation from the base's plane is 45 degrees. Calculate its surface area. - 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. - Identical 35961
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? - 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
- Body diagonal
Calculate the volume of a cuboid whose body diagonal u equals 6.1 cm. The rectangular base has dimensions of 3.2 cm and 2.4 cm. - 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. - Calculate diagonals
Calculate the length of the solid diagonals of a prism with a rhombus base if the sizes of the base diagonals are 16 cm and 20 cm and the height of the prism is 32 cm. Calculate the size of the base edge. - 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.
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