Solid geometry, stereometry - page 107 of 123
Number of problems found: 2442
- Container height
A cylindrical container with a bottom diameter of 30 cm and a height of 20 cm is filled with water. We want to pour the water into another cylindrical container with a bottom diameter of 15 cm. What minimum height must the second container have for the wa - Cube construction
A 2×2×2 cube will be constructed using four white and four black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. ) - Largest wall
Find the area of the largest wall of a prism with a rectangle base with a height of 4 dm, side c = 5 cm, and side b = 6 cm. - Copper wire
What is the weight of 1000 m copper wire with a diameter of 5 mm when metric density p = 8.8 g/cm³? - Dice in a box
In a box in the shape of a cuboid, four kinds of dice are stored in four layers. In the first layer there are dice with an edge length of 12 cm. In each subsequent layer the length of the edge of the die is 2 cm smaller than the length of the edge of the - Cone Radius Sector Angle
Determine the cone's base's radius if its shell develops into a circular section with radius "s" = 10 and center angle x = 60 °. r = ?, o =? - Tower roof
The tower's roof is a regular 4-sided pyramid with a height of 4 m and an edge of the base of 6 m. 25% of the roof covering was found to be damaged. How many square meters of coverage are needed to repair the roof? - Tower
The roof of the tower is a regular hexagonal pyramid with a base edge 5.7 meters long and a height 7 meters. How many m² of the sheet is required to cover the top of the tower? We must add 4% of metal for waste. - Cube surfaces ratio
The volumes of the two cubes are in the ratio of 27:8. What is the ratio of the surfaces of these cubes? - Sphere vs cube
How much % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere? - Aquarium water liters
We are to fill an aquarium with a bottom dimension of 30 cm x 30 cm with water. How many liters of water will we need if we pour water to a height of 20 cm? - Cube substance density
What kind of substance is it if it is enclosed in a cube with a volume of 8 m³ weighing 110 kg and the filled cube weighs 115.78 kg? - Billiard balls
A layer of ivory billiard balls radius of 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to everyone adjacent to it. In the spaces between sets of 4 adjacent balls, other balls rest, equal in size to the original. - 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. - Tent
A pyramid-shaped tent has a base square with a side length of 2 m and a height of 1.7 m. How many meters of canvas is needed to make it if we should add 10% for waste? - Bottles of juice
How many 2-liter bottles of juice need to buy if you want to transfer the juice to 50 pitchers' rotary cone shape with a diameter of 24 cm and a base side length of 1.5 dm? - 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 - 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. - Calculation - mesh
Sketch the mesh of a cylinder whose base radius to height ratio is 2 : 3. Calculate the volume and surface of the cylinder if its height is 9 cm (sketch, calculation, answer). - Cylinder in Cone Volume
A cylinder with a height equal to half the height of the cone is inscribed in the rotating cone. Find the volume ratio of both bodies.
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