Solid geometry, stereometry - page 102 of 121
Number of problems found: 2402
- Water level
To cuboid-shaped poll, bottom size 2m and 3.5m, flows water at a rate of 50 liters per minute. How long will it take for water to reach a level of 50 cm? - Cuprum
From the 1600 mm long sheet of copper plate 2 mm thickness, we have separated over the whole length of the belt weighing 6000 g. Calculate belt width if one dm³ copper weighs 8.9 kg. - TV transmitter
The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have - Cube in ball
The cube is inscribed into the sphere of radius 181 dm. How many percent is the volume of the cube of the volume of the sphere? - 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. - Cube wall
The surface of the first cube wall is 64 m². The second cube area is 40% of the surface of the first cube. Find the length of the edge of the second cube (x). - Length 6208
How does the volume of a cube change if we double the length of its edge?
- Inscribed sphere
How much percent of the cube volume takes the sphere inscribed into it? - What quantity
What quantity of concrete should be ordered for concreting a rectangular family house with dimensions of 15 m × 12.6 m using permanent formwork? The depth of the foundation formed by permanent formwork is set at 80 cm. The concrete used constitutes 80% of - Stone
When Peter threw a stone in a water box, he discovered that the water level had risen by 6 cm. The box has a cuboid shape, the bottom has dimensions of 24 cm and 14 cm, height is 40 cm. What volume has a stone? - Medal
Calculate the approximate weight of the gold Olympic medal if its diameter is 7 cm and its thickness 6 mm. The density of gold can be found in tables or on the Internet. - Pyramid-shaped 7820
The pyramid-shaped tent has a square base with a side size of 2.2m and a height of 1.8m. How many square meters of tent canvas are needed to make it if we count an extra five percent for the foundation? - Wood material
Calculate the weight of a block measuring 15 cm, 7.5 cm, and 10 cm made of: a) oak wood (ρ = 800 kg/m³), b) spruce wood (ρ = 550 kg/m³). - The glass
1 m³ of glass weighs 2600 kg. Calculate the weight of the glass glazing panel with dimensions of 2.5 m and 3.8 m if the thickness of the glass is 0.8 cm. - 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?
- Needed 5373
The box is shaped like a cube with an edge 52 cm long. How many m² of sheet metal is needed to make a box with a lid? Add 5% to the folds of the lid and walls. - Four-sided 7910
The roof of the recreation cottage has the shape of a regular four-sided pyramid with a height of 8m and a base edge of 4m. How much ℅ went to folds and joints, and 75.9 square meters of sheet metal were used to cover the roof? - Cutting cone
A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm. - Volume of sphere
How many times does the volume of a sphere increase if its radius increases two times? - Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in the corner of a room. The spheres are each tangent to the walls and floor an
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