Pythagorean theorem + cube root - practice problems
Number of problems found: 22
- Moivre 2
Find the cube roots of 125(cos 288° + i sin 288°). - Equilateral cone
We pour so much water into a container with the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down? - Cubes
One cube is an inscribed sphere, and the other one is described. Calculate the difference of volumes of cubes if the difference of surfaces in 231 cm². - Cube in a sphere
The cube is inscribed in a sphere with a volume 7253 cm³. Determine the length of the edges of a cube. - 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. - Body diagonal
The cuboid has a volume of 32 cm³. Its side surface area is double as one of the square bases. What is the length of the body diagonal? - Diagonals 5551
The cube has a wall area of 81 cm². Calculate the length of its edge, wall, and solid diagonals. - 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? - Millimeter 24231
Calculate the length of the wall diagonal of a cube with a volume of 7.40 square meters. Express the result to the nearest millimeter. - Body diagonal
Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonally. - Calculate 83044
The cube comprises 64 small cubes, each with an edge length of 15 mm. Calculate the wall length and body diagonals. - Calculate 6214
The cube A B C D A'B'C'D 'has a section area ACC'A' equal to 64 square root of 2 cm². Calculate the surface of the cube. - Inscribed 81949
A cube is inscribed in a sphere with a radius of 27 cm. Calculate its volume and surface area. - An equilateral cone
Determine the radius and height (in centimeters) of an equilateral cone that has a volume of 1 liter. - Cube diagonals
Calculate the length of the side and the diagonals of the cube with a volume of 27 cm³. - Calculate 82458
Calculate the volume of a cube with a wall diagonal of u = 20 cm. - Cube - wall
V kocke ABCDEFGH je |CF|=4 √ 2. Aký je povrch kocky? - Calculate 64654
Calculate the length of the wall and body diagonal in a cube with an edge of 60 cm. - Body diagonal
Calculate the volume and surface of the cube if the diagonal body measures ten dm. - Calculate
Calculate the length of the wall diagonal of the cube with an edge 5 cm long.
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