Solid geometry, stereometry - page 109 of 123
Number of problems found: 2442
- Quadrilateral shelter
The shelter has the shape of a regular quadrilateral pyramid without a front wall. The length of the base edge is 3 meters, and the shelter's height is 3.5 meters. How much canvas must be bought to sew it if we have to increase consumption by 20% for fold - Column water force
A concrete column with a density of 3500 kg/m3, a height of 6 m, and a square base of a=25 cm lies at the bottom of the dam at a depth of 10 m. At the upper end, it is lifted by a rope by a crane. 1) with how much force does the pole stretch th - Jakub 6
Jakub collects dice, all of the same size. Yesterday he found a box into which he began to place the dice. The first layer covered exactly the square bottom of the box. He placed five more layers similarly, but in the middle of the next layer the dice ran - Area and percents
Find what percentage is a smaller cube surface when the wall's surface area decreases by 25%. - Two cuboids
A cuboid has dimensions of 2 m × 3 m × 4 m. We increase the length of all edges by 50 cm. 1. By what percentage does the surface area of the cuboid increase compared to the original? Round the result to the nearest whole percent. 2. By what percentage doe - Dimensions - crate
A wooden crate with dimensions d=3 m, e=4 m, and f=3 m was placed in a transport container with dimensions a=10 m, b=4 m, and c=3 m. What is the maximum length of a straight, rigid rod of negligible diameter that can still be placed in the container in th - Hexagonal packaging
The cardboard packaging without a lid has the shape of a regular hexagonal prism with a main edge that is 12 cm long and 15 cm high. How much cardboard is used to make five packages if 10% of the cardboard is added for folds? Give results in square decime - Tropics and polar zones
What percentage of the Earth's surface lies in the tropical, temperate, and polar zones? Tropics border individual zones at 23°27' and polar circles at 66°33'. - The truncated
The truncated rotating cone has bases with radii r1 = 8 cm, r2 = 4 cm, and height v = 5 cm. What is the volume of the cone from which the truncated cone originated? - 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. - Cylinder surface, volume
The area of the base and the area of the shell are in the ratio of 3:5. Its height is 5 cm less than the radius of the base. Calculate both surface area and volume. - Wooden
A wooden cube with an edge of 12 cm is painted with red paint. After the paint dries, the cube is cut into small cubes with an edge of 2 cm. Write how many small cubes will have exactly two red faces. - Tetrahedron water level
A container shaped like a rotating cylinder with a base radius of 5 cm is filled with water. If a regular tetrahedron with an edge of 7 cm is immersed in it, how much will the water level in the container rise? - Cuboid - edges
The cuboid has dimensions in a ratio of 4:3:5. The shortest edge is 12 cm long. Find: The lengths of the remaining edges The surface of the cuboid The volume of the cuboid - Radiators
Calculate the radiator output if it has a thermal gradient (difference between inlet water and return temperatures) a) 5 °C b) 10 °C c) 15 °C d) 20 °C A heating water volume flow is 45 kg/h. How fast the water flows from the supply pipe to the radiator e) - Cone sphere volume
A sphere is inscribed in an equilateral cone with a base diameter of 12 cm. Calculate the volume of both bodies. What percentage of the volume of the cone is filled by the inscribed sphere? - Pizza
Pizza with a diameter of 40 cm weights 409 g. What diameter will a pizza weigh 764 g made from the same cloth (same thickness) and decorated? - Axial section
The axial section of the cylinder is diagonal 45 cm long, and we know that the area of the side and the base area are in the ratio 6:5. Calculate the height and radius of the cylinder base. - Wooden prism
The wooden prism weighs 5 kg and has a 700 kg/m³ density. Calculate the volume of the wooden prism. - Ratio 52 The ratio of the surface area of a cube to its volume is 2:1. Calculate: a) the edge length of the cube in cm, b) the volume of the cube in cm³, c) the surface area of the cube in cm².
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