Solid geometry, stereometry - page 107 of 121
Number of problems found: 2409
- Prism
A right-angled prism, whose base is a right triangle with leg a = 3 cm and hypotenuse c = 6 cm, has the same volume as a cube with an edge length of 1 dm. a) Find the height of the prism b) Calculate the surface of the prism c) What percentage of the cube - Kitchen tiles
We want to cover all the kitchen walls with square tiles with a side of 15 cm up to a height of 1.2 m. The kitchen has two doors, the frames of which are 90 cm wide. How many tiles will we buy if we expect a loss of 5% and the floor's dimensions are 3.2 m - Cube edge reduction
If we reduce the length of the cube edge by 30%, this cube has a reduced surface area of 1176 cm². Find the edge length and volume of the original cube. - Prism volume calculation
The prism with a diamond base has one base diagonal of 20 cm and a base edge of 26 cm. The edge of the base is 2:3 to the height of the prism. Calculate the volume of the prism. - Block edge dimensions
How many blocks have integer dimensions of the edges if the surface is 48 m²? - 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) DN1 - Ribbon on the cube
A cubical gift box is tied with a piece of ribbon. If the total length of the free ends and the bow is 18 inches, what is the length of the ribbon used? (Each side of the cube is 6 inches). - Cylinder - h2
The cylinder volume is 3 liters. The base area is 1.1 dm². Calculate the height of the cylinder. - Tower Sheet Metal Coverage
The tower has the shape of a regular four-sided pyramid with a base edge of 0.8 m. The height of the tower is 1.2 meters. How many square meters of sheet metal is needed for coverage if we count eight percent for joints and overlap? - Cylindrical tank
The cylinder-shaped tank with a diameter of 100 cm is 50% full and contains 7850 l of water. What is the height of the tank? - Pyramid Roof Sheet Metal
The roof of the recreation cottage has the shape of a regular four-sided pyramid with a height of 8m and a base edge of 4m. How much ℅ went to folds and joints, and 75.9 square meters of sheet metal were used to cover the roof? - Ratio of edges
The cuboid dimensions are in a ratio of 3:1:2. The body diagonal has a length of 28 cm. Find the volume of a cuboid. - CuZn
Brass is an alloy of copper and zinc. The 10-centimeter brass cube weighs 8.6 kg. Copper density is 8930 kg/m3, the zinc density is 7130 kg/m³. Calculate how many kilograms of copper and zinc a cube contains. - Ice layer
A 2 cm thick layer of ice formed in the circular water tank. What part of the tank's water (answer in percent) froze if the tank has a diameter of 20 m and a depth of 1.5 m? - Block material calculation
How many square meters of material is needed to make two identical blocks with dimensions of 6 dm, 8 dm, and 12 dm if we count 8% of the material for folds? (Round to two decimal places. ) - 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 - Cup Diameter Ball Displacement
The mug has the shape of a cylinder with a height of 60.7 mm. There is two dl of water in it. If we dip a ball with a diameter of 40 cm into the water, the water will not overflow. What is the minimum diameter of the cup? - Isosceles weight
A designer weight is made from a glass cube by cutting a three-sided prism with an isosceles triangle base that is right-angled and whose arm is half the length of the cube edge. What percentage of the cube is cut off when making the weight? - Cuboid face diagonals
The lengths of the cuboid edges are in the ratio 1:2:3. Will the lengths of its diagonals be in the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid. - Ratio-cuboid
The lengths of the edges of the cuboid are in the ratio 2:3:6. Its body diagonal is 14 cm long. Calculate the volume and surface area of the cuboid.
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