Solid geometry, stereometry - page 111 of 121
Number of problems found: 2409
- Logs
The trunk diameter is 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. - Cube volume comparison
We have two cubes of the same weight. One is all made of glass, the other of cork. Which one has more volume, and how many times? - 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. - 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. - Truncated cone
Calculate the height of the rotating truncated cone with volume V = 1471 cm³ and a base radii r1 = 6.1 cm and r2 = 7.9 cm. - 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. - 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 - 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. - 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. - Ice cube weight
The sculptor composes an ice city from ice cubes. The cube with an edge length of 2 dm weighs 7.2 kg. How many kilograms is an ice cube with an edge length of 6 dm heavier than it? - Brass tube
The outer perimeter of the brass tube (ρ = 8.5 g/cm³) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness? - 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. - 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. - 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? - MO SK/CZ Z9–I–3
John had the ball that rolled into the pool and swam in the water. Its highest point was 2 cm above the surface. The circle's diameter that marked the water level on the ball's surface was 8 cm. Find the diameter of John's ball. - Monument weight
A granite monument in the shape of a pyramid with a rectangular base will be placed in the city park. The base dimensions are 60 cm and 110 cm, and the pyramid height is 220 cm. The density of granite is approximately 2800 kg/m³. Calculate the weight of t - A raft
I want to build a raft, and I have beams with a square section with side a=20cm and length l=2m, wood density 670 kg/m³. I will connect 10 beams - what is the volume of the raft and its weight? How deep will a raft sink in water (water density 1000kg/m³)? - Quadrilateral pyramid
The volume of a regular quadrilateral pyramid is 72 cm³. Its height is equal to the length of the base edge. Calculate the length of the base and the surface of the pyramid.
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