Solid geometry, stereometry - page 113 of 123
Number of problems found: 2442
- Transforming cuboid
A cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length? - Quadrilateral pyramid
The volume of a regular quadrilateral pyramid is 72 cm³. Its height is equal to the length of the base edge. Calculate the length of the base and the surface of the pyramid. - Slant surface
The surface of the rotating cone and its base area is in the ratio 18:5. Determine the volume of the cone if its body height is 12 cm. - Cuboid - ratios
The sizes of the edges of the cuboid are in the ratio of 2:3:5. The smallest wall has an area of 54 cm². Calculate the surface area and volume of this cuboid. - Air mass
What is the mass of the air in a classroom with dimensions 10 m × 3 m × 3 m? The density of air is 1.293 kg/m³. - Cylinder surface
The area of the rotating cylinder shell is half the area of its surface. Calculate the surface of the cylinder if you know that the diagonal of the axial section is 5 cm. - Rope
How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and a length of 350 mm (the central mandrel has a diameter of 50 mm)? - Ice cube weight
The sculptor composes an ice city from ice cubes. The cube with an edge length of 2 dm weighs 7.2 kg. How many kilograms is an ice cube with an edge length of 6 dm heavier than it? - Brass tube
The outer perimeter of the brass tube (ρ = 8.5 g/cm³) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness? - Truncated cone
Calculate the height of the rotating truncated cone with volume V = 1471 cm³ and a base radii r1 = 6.1 cm and r2 = 7.9 cm. - Tower
Charles built a tower of cubes with an edge 2 cm long. In the lowest layer, there were six cubes (in one row) in six rows. In each subsequent layer, always one cube and one row less. What volume in cm³ did the whole tower have? - Cube volume comparison
We have two cubes of the same weight. One is all made of glass, the other of cork. Which one has more volume, and how many times? - Cube painting
Entrepreneur Kostkoš wanted to produce colorful blocks for schools. But he gave them to another businessman to paint, who asked €1,117.2 for painting 1,000 cubes. The area that needs to be painted on one cube is 294 square centimeters. Please write how ma - Volume and surface
Calculate the volume and surface area of the cylinder when the cylinder height and base diameter are in a ratio of 3:4, and the area of Lateral Surface Area (LSA) is 24 dm². - Cone and the ratio
The rotational cone has a height of 59 cm, and the ratio of the base surface to the lateral surface is 10: 12. Calculate the surface of the base and the lateral surface. - Two cubes 3
Two cubes made of plasticine have single-digit integer edge lengths differing by 1 cm. Can a single larger cube with an integer edge length be made from the same total amount of plasticine? - Pyramid model
Peter brought back from his vacation in Egypt a model pyramid in the shape of a regular quadrilateral pyramid. He measured that its base edge has a length of 7 cm and the lateral edge has a length of 10 cm. The model has a mass of 1 kg and is made of an u - Larger sphere
The volume of the sphere is 20% larger than the volume of the cone. Find its surface if the volume of the cone is 320 cm³. - Rectangle pool
Find the dimensions of an open pool with a square bottom and a capacity of 32 m³ that can have painted/bricked walls with the least amount of material. - Cuboid and ratio
A cuboid has dimensions in a ratio of 1:2:6, and the surface area of the cuboid is 1000 dm². Calculate the volume of the cuboid.
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