Space diagonal - practice problems - page 3 of 6
Remember: Solve each problem thoughtfully and make sure to show your complete solution for every question.Number of problems found: 115
- 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 - 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. - Sphere cube filling
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? - Block measurements
Calculate the solid diagonal of a block whose dimensions are: a = 3cm, b = 5, c = 7cm. Find its volume as well. - 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. - Suitcase - rod
The trunk of a car has the shape of a cuboid with sides 1.6m x 1.2m x 0.5m (width, depth, height). Determine the longest thin rod that can be placed on the bottom. - Cube measurements
The cube has a wall area of 81 cm². Calculate the length of its edge, wall, and solid diagonals. - Cube diagonals
If you know the length of the body diagonal u = 216 cm, determine the cube's volume and surface area. - 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. - Totem shed fitting
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? - Cuboid's diagonal
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? - 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? - 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? - Block diagonal length
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. - 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. - Cube dimension calculation
The cube has an area of 486 dm². Calculate the length of its side, its volume, the length of the body, and wall diagonals. - 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. - 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. - Whistle fit
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? - Cube triangle volume
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?
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