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: 118
- Cuboid
Find the dimensions a, b, and c of a cuboid whose space diagonal is d = 6 dm and makes an angle α = 35° with edge a and an angle β = 66° with edge b. - Trunk
Calculate the length of the longest fishing rod that can be placed in a car boot with dimensions 152 × 82 × 81 cm. - Ratio-cuboid
The edges of a cuboid are in the ratio 2:3:6. Its space diagonal is 14 cm long. Calculate the volume and surface area of the cuboid. - 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. - 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? - 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? - 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? - Cube measurements
The cube has a wall area of 81 cm². Calculate the length of its edge, wall, and solid diagonals. - 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? - 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 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. - Diagonal
Determine the dimensions of a cuboid whose space diagonal is 60 dm and makes an angle of 35° with one edge and 77° with another edge. - 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? - Tetrahedral pyramid
It is given a regular tetrahedral pyramid with a base edge of 6 cm and a height of pyramid 10 cm. Calculate the length of its side edges. - Box wand fit
The box has dimensions of 30 cm, 40 cm, and 120 cm. Will a 128 cm long wand fit in it? - 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?
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