Solid geometry, stereometry - page 106 of 121
Number of problems found: 2418
- 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. ) - Cone mesh drawing
Sketch the cone mesh and add the side length, the arc length of the circle, and the circle length to it, if you know: the side length of the cone: s = 51.9 cm cone base circumference = O = 151 mm. - Perimeter of needle
The perimeter of the four-sided needle is 48 m, and its height is 2.5 m; how much will the sheet metal for this pyramid cost? If 1m² costs €1.5, a 12% loss due to joints and folds is included in the area. - How many
How many m² of copper sheet is needed to replace the roof of a conical tower with a diameter of 13 meters and a height of 24 meters if we count 8% of the material for bending and waste? - The observatory
The dome of the hemisphere-shaped observatory is 5.4 meters high. How many square meters of sheet metal need to be covered to cover it, and must we add 15 percent to the minimum amount due to joints and waste? - Rectangle dimensions
The rectangle has a circumference of 24 cm so that its area is maximum and its length is larger than its width. Find the dimensions of a rectangle. - 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? - 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 entire cube weighs 115.78 kg? - Earth's surface
The greater part of the Earth's surface (r = 6371 km) is covered by oceans; their area is approximately 71% of the Earth's surface. What is the approximate area of the land? - Gold Cube Weight
How much does a gold cube weigh, 30 x 30 x 30 cm? - Four-sided turret
The turret has the shape of a regular four-sided pyramid with a base edge 0.8 m long. The height of the turret is 1.2 m. How many square meters are needed to cover it, counting the extra 10% sheet metal waste? - Pyramid-shaped roof
A block-shaped shed is covered with a quadrilateral pyramid-shaped roof with a base with sides of 6m and 3m and a height of 2.5m. How many m² (square meters) must be purchased if an extra 40% is calculated for roofing and waste? - Conical bottle
When a conical bottle rests on its flat base, the water in the bottle is 8 cm from its vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle? - 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. - Granite cube statue
What is the weight of a granite cube with an edge length of 75 cm if one m³ of granite weighs 2.7 tons? - 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. - 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 - Frustum of a cone
A reservoir contains 28.54 m³ of water when complete. The diameter of the upper base is 3.5 m, while the lower base is 2.5 m. Find the height if the reservoir is in the form of a frustum of a right circular cone. - 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?
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