Solid geometry, stereometry - page 109 of 121

Number of problems found: 2404

Cube cut
The edge of the CC' guides the ABCDA'B'C'D'cube, a plane that divides the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine which ratio the edge AB divides by this plane.
Right-angled 25091
A thin plate in the shape of a right-angled triangle is turned once around the shorter hanger and a second time around the longer hanger. Cones are described by rotation. Are they the same volume? The dimensions are: shorter pendant 6cm, longer pendant 8c
Calculate 19543
Calculate the surface of a prism with a square base whose mantle is a rectangle with sides of 18cm and 8cm. How many solutions does the task have? List all solutions.
Equilateral 81222
A sphere is inscribed in an equilateral cone with a base diameter of 12 cm. Calculate the volume of both bodies. What percentage of the volume of the cone is filled by the inscribed sphere?
Diameter 3962
The diameter of the atomic nucleus is 10 to -12cm. How many atoms would fit on a 1 mm line if they could be arranged close together?
Hollow sphere
The hollow steel sphere floats on the water, plunged into half its volume. Determine the outer radius of the sphere and wall thickness if you know that the weight of the sphere is 0.5 kg and the density of steel is 7850 kg/m³
Confectionery 7318
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.
Calculate 81935
The volume of the cuboid is 960 cm³. The lengths of the edges are in the ratio 1 : 3: 5. Calculate the surface area of the cuboid.
Maximum of volume
The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum?
Sphere and cone
Within the sphere of radius G = 33 cm, inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone?
Calculation 83339
The edges of a cuboid are in the ratio 1:2:3. Calculate their length if you know that the surface of the entire cuboid is S=5632 m². Then, perform a test to ensure the calculation is correct.
Larger sphere
The volume of the sphere is 20% larger than the volume of the cone. Find its surface if the volume of the cone is 320 cm³.
Decreases 5625
How much percent will the surface and volume of the cube decrease if the diagonal decreases by 10%? b) if the diagonal increases by 10%?
Calculate 81936
The volume of the block is 7,500 dm³. The lengths of the edges are in the ratio 3: 4: 5. Calculate the surface area of the cuboid.
Triple density
How many times does the density of a steel pipe increase if we triple its length?
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?
Calculate 82808
Calculate the radius of an iron ball with a density of 7.8g/cm³ and a mass of 7kg.
Observation tower
The observation tower is covered with a roof in the shape of a regular quadrangular pyramid with a base edge of 8 m and a height of 6 m. 60% of the roofing needs to be replaced. How many m² do you need to buy?
Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base of 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure.
Compressive 4894
At what depths does a hydrostatic compressive force of 3 kN act at a depth of 30 m in water?

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