Solid geometry, stereometry - page 112 of 123
Number of problems found: 2442
- Cone cutout
The cone shell with a base radius of 20 cm and a height of 50 cm unfolds into a circular cutout. How big is the center angle of this cutout? - Metal balls
Four metal balls with a diameter of 5 cm are placed in a measuring cylinder with an inner diameter of 10 cm. What is the smallest water volume to be poured into the cylinder so that all balls are below the water level? - Logs
The trunk has a diameter of 52 cm. Is it possible to inscribe a square prism with a side 27 cm? - Rectangular cuboid
The rectangular cuboid has a surface area 4131 cm², and its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid. - Cork weight
The cork has a diameter of 20 mm and is 38 mm high. How many plugs will weigh 1 kg/cork density = 0.3 g / cm cubic /. - Similarity
Rectangle ABCD has dimensions of 7 cm and 8 cm. Rectangle PQRS has dimensions 7 cm and 6 cm. Determine the coefficient of the similarity k of the rectangles; if they aren't similar, enter zero as the coefficient of similarity. - Iron ball
Calculate the radius of an iron ball with a density of 7.8 g/cm³ and a mass of 7 kg. - Cube edges length
If we reduce the length of the cube edge by 30%, this reduced cube has an area of 1176 cm². Specify the edge length and volume of the original cube. - Two bodies
The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Find the ratio of surfaces of the first and second bo - Prism bases
Volume perpendicular quadrilateral prism is 360 cm³. The edges of the base and height of the prism are in the ratio 5:4:2. Find the area of the base and walls of the prism. - Three-sided prism
Find the area of the largest wall of a three-sided prism, with a height of 4 dm and an edge length of 5 cm and 6 cm. - Triangle rotation volume
The rotating body was created by rotating an equilateral triangle with a side length of a=2 cm around one of its sides. Calculate the volume of this rotating body. - Quadrilateral 4S prism
The edge lengths of a quadrilateral prism are in the ratio a:b:c = 2:4:5. The surface of the prism is 57 cm². Calculate the volume. - Largest possible cone
It is necessary to make the largest possible cone from an iron rod in the shape of a prism with dimensions of 5.6 cm, 4.8 cm, and 7.2 cm. a) Calculate its volume. b) Calculate the waste. - 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. - Confectionery
The confectioner needs to carve a cone-shaped decoration from a ball-shaped confectionery mass with a radius of 25 cm. Find the radius of the base of the ornament a (and the height h). He uses as much material as possible is used to make the ornament. - Lampshade
The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm² of material will we need when 10% is waste? - Cube edge ratio
The lengths of the edges of two cubes are in the ratio 1:2, determine: a) the ratio of the area of the wall of the smaller cube to the area of the wall of the larger cube. b) the ratio of the surface of the smaller cube to the surface of the larger cube. - Perfect cubes
Suppose a number is chosen at random from the set (0,1,2,3,. .. ,202). What is the probability that the number is a perfect cube? - Pyramid stone weight
The largest Egyptian pyramid has the shape of a regular four-sided pyramid with a base edge of approximately 227 meters and a height of about 140 meters. How many tons of stone did the workers transport to build it? One cube of stone weighs 2500 kg and ne
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