Space diagonal - practice problems - page 2 of 6
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 114
- Cuboid face diagonals
The lengths of the cuboid edges are in the ratio 1:2:3. Will the lengths of its diagonals be in the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid. - Ratio of edges
The cuboid dimensions are in a ratio of 3:1:2. The body diagonal has a length of 28 cm. Find the volume of a cuboid. - 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. - 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. - 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. - Two balls
Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them. - 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.
- 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 wall
Calculate the cube's diagonal if you know that one wall's surface equals 36 centimeters square. Please also calculate its volume. - Body diagonal
Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonally. - Cube diagonals
If you know the length of the body diagonal u = 216 cm, determine the cube's volume and surface area. - Dimensions 6264
Calculate the length of the body diagonal of a block whose dimensions are a = 5cm, b = 6cm, c = 10cm. - 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. - Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in the corner of a room. The spheres are each tangent to the walls and floor an - Block-shaped 39241
The boys wanted to store their hand-made totem 5.1 m high in the block-shaped shed, which measures 4 m, 3 m, and 2 m, for the winter. Will it fit in there at all?
- 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. - 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.
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