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
- 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. - 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°. - 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? - Ratio-cuboid
The lengths of the edges of the cuboid are in the ratio 2:3:6. Its body diagonal is 14 cm long. Calculate the volume and surface area of the cuboid. - Diagonals 5551
The cube has a wall area of 81 cm². Calculate the length of its edge, wall, and solid diagonals. - Dimensions 3950
Calculate the solid diagonal of a block whose dimensions are: a = 3cm, b = 5, c = 7cm. Find its volume as well. - Cuboidal room
The length of the cuboidal room is 2m the breadth of the cuboidal room is 3m and height is 6m find the length of the longest rod that can be fitted in the room - Angle of diagonal
The angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume. - Body diagonal
The cuboid has a volume of 32 cm³. Its side surface area is double that of one of the square bases. What is the length of the body diagonal? - Cube diagonals
If you know the length of the body diagonal u = 216 cm, determine the cube's volume and surface area. - Prism
A right prism's length, width, and height are 17, 11, and 11, respectively. What is the length of the longest segment whose endpoints are vertices of the prism? - 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. - 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? - 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? - Diagonal 8192
Find the volume and surface of a cube if you know the length of its body diagonal u = 216 cm. - Dimensions 6264
Calculate the length of the body diagonal of a block whose dimensions are a = 5cm, b = 6cm, c = 10cm. - 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. - Centimeters 3940
Calculate the solid diagonal of a cube whose surface equals 24 square centimeters. - 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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