Pythagorean theorem + cube - practice problems
Number of problems found: 62
- Moivre 2
Find the cube roots of 125(cos 288° + i sin 288°). - Chocolate roll
The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the identical chocolate roller of a prism shape with a length of 0.5 m whose cross-section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm? You know that 100 g of - 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 from sphere
What largest surface area (in cm²) can have a cube that we cut out of a sphere with a radius 26 cm? - Prism
A right-angled prism, whose base is a right triangle with leg a = 3 cm and hypotenuse c = 13 cm, has the same volume as a cube with an edge length of 3 dm. a) Find the height of the prism b) Calculate the surface of the prism c) What percentage of the cub - 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 - 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.
- Cube wall
Calculate the cube's diagonal if you know that one wall's surface is equal to 36 centimeters square. Please also calculate its volume. - 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? - Pyramid in cube
In a cube with an edge 12 dm long, we have an inscribed pyramid with the apex at the center of the cube's upper wall. Calculate the volume and surface area of the pyramid. - Quadrilateral 46431
Calculate the volume V and the surface S of a regular quadrilateral pyramid, the base edge and height of which are the same size as the edge of a cube with a volume V1 = 27m3 - Diagonals 5551
The cube has a wall area of 81 cm². Calculate the length of its edge, wall, and solid diagonals.
- Truncated cone 6
Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1. - Cube diagonals
Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm. - Diagonal 8192
Find the volume and surface of a cube if you know the length of its body diagonal u = 216 cm. - Decimetres 4163
Determine the length of the body and wall diagonals of the cube, the volume of which is equal to 0.343 decimetres. Also, calculate its surface. - 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.
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