Solid geometry, stereometry - page 98 of 121
Number of problems found: 2409
- The wooden
The wooden block measures 12 cm, 24 cm, and 30 cm. Peter wants to cut it into several identical cubes. At least how many cubes can he get? - Cylinder
A 1-meter diameter cylinder is 1413 liters of water, which is 60% of the cylinder. Calculate the cylinder height in meters, do not write the units. Please the resulting value round and write it as an integer. - Cellar pump drainage
The cellar, which has a floor area of 50 m² and is 3 m below ambient level, was flooded with water to a height of 80 cm. How long does it take for a pump with a power input of 1 kW and an efficiency of 75% (η = 0.75) to drain the water? - Minimum surface
Find the length, breadth, and height of the cuboid-shaped box with a minimum surface area into which 50 cuboid-shaped blocks, each with length, breadth, and height equal to 4 cm, 3 cm, and 2 cm, respectively, can be packed. - Prism pyramid ratio
For the volumes of a perpendicular prism and a pyramid with the same base and height: A) the volumes are equal B) the volume of a pyramid is three times smaller than the volume of a prism C) the ratio of the volumes of the prism and the pyramid is 1:3 D) - Surface area 2
Calculate how many % reduce the surface area of the cube is reduced the length of each edge by 10%. - 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? - The room
The room has a cuboid shape with dimensions: length of 50m and width of 60 dm, and height of 300 cm. Calculate how much this room will cost (a floor is not painted) if the window and door area is 15% of the total area and 1m² costs 15 euros. - Cube
One cube has an edge increased five times. How many times will larger its surface area and volume? - Metal sheet
The box has the shape of a cube with an edge length of 50 cm. How much m² of sheet metal is needed to beat a box if we add 20% on the folds of the lid and walls? - Cube paper calculation
Calculate how much cm² of paper needs to be bought to make a 60 mm cube if you need to add an extra 12% to the folds. - Original model
When drying, the modeling mass loses 36% of its original volume. If the cube's volume is 5.12 dm³ after drying, what was the original length of the edge? - Cube wall coloring
We color a wooden cube with an edge length of 3 cm so that three walls are blue, three are red, and no two opposite walls are the same color. Cut the cube into 1 cm³ cubes. How many cats will have at least one red wall and at least one blue wall? - Reduce of the volume Calculate how many % reduce the volume of the cube is reduced the length of each edge by 10%.
- Painting
The room is 50 meters long, wide 60 dm, and 300 cm high. Calculate how much it will cost to paint if the area of windows and doors is 15% of the total area. One square meter costs 50 cents. - Cuboid 5
Calculate the mass of the cuboid with dimensions of 12 cm, 0.8 dm, and 100 mm made from spruce wood (density ρ = 550 kg/m³). - Percentage + sphere
A sphere G is inscribed in the cube K with the length a. A cube K1 is inscribed in sphere G. What percentage of the volume of cube K is made up of the volume of cube K1? - Wooden board weight
What is the weight of a wooden board 1.8 m long, 70 cm wide, and 5 cm high? The density of wood is p = 450 kg/cubic meter. - Roof material
In the form of a pyramid on the house with a square floor plan, the roof has dimensions of 12 x 12 m, with a height of 2 m at the highest point. How much roofing do I need to buy? Count on a 10% reserve. - Cement foundation
How many kilograms of cement are used to concrete the foundations under the machine if the concrete slab has the shape of a cuboid 4.6 m long, 2.7 m wide, and 45 cm high if 250 kg of cement is used per 1 m³?
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