Area + space diagonal - practice problems
Number of problems found: 42
- Calculate 415
Calculate the cuboid's dimensions if the sum of its edges is 19cm. The body's diagonal size is 13 cm, and its volume is 144 cm³. The total surface area is 192 cm². - Calculate 82567
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. - ABCDEFGH 82499
In the cube ABCDEFGH, the area of triangle ABK is √20 cm². How much cm² is the volume of ABGH in a cube if you know that K is the midpoint of edge CG? - Quadrilateral 82146
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.
- Inscribed 81949
A cube is inscribed in a sphere with a radius of 27 cm. Calculate its volume and surface area. - Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and the body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - 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. - Cuboid diagonals
The cuboid has dimensions of 15, 20, and 40 cm. Calculate its volume and surface, the length of the body diagonal, and the lengths of all three wall diagonals. - Calculate 32133
The cube has an area of 486 dm². Calculate the length of its side, its volume, the length of the body, and wall diagonals.
- 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. - Regular hexagonal prism
Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long. - Calculate 24201
Calculate the surface area, volume, and length of the body diagonal of a cube with an edge length of 4 dm. - 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°. - Space diagonal
The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area, and volume of the cube.
- Height of the room
Given the floor area of a room as 24 feet by 48 feet and the space diagonal of a room as 56 feet. Can you find the height of the room? - Diagonal 8192
Find the volume and surface of a cube if you know the length of its body diagonal u = 216 cm. - 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? - Cube diagonals
The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal. - Body diagonal
Calculate the volume and surface of the cube if the diagonal body measures ten dm.
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