Volume + space diagonal - practice problems
Number of problems found: 56
- 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 83044
The cube comprises 64 small cubes, each with an edge length of 15 mm. Calculate the wall length and body diagonals. - 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. - One-third 77724
The cuboid has a body diagonal u=25 cm, and side b is one-third longer than side a. What is the volume of the cuboid? - Measuring 65374
Calculate the length of the body diagonal of a block measuring 6 cm, 7 cm, and 10 cm, and round the result to two decimal places. - Calculate 64654
Calculate the length of the wall and body diagonal in a cube with an edge of 60 cm.
- 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. - Identical 35961
Nine identical spheres are stacked in the cube to fill the volume of the cube as much as possible. What part of the volume will the cube fill? - 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. - Measures 23791
The volume of the block is 144 cm³. The base measures 3 cm and 4 cm. How big is the body diagonal? - 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?
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