Solid geometry, stereometry - page 109 of 121
Number of problems found: 2409
- The iron roller
The iron roller has a base circumference of 28 π cm. The worker drilled a hole through the top of the roller. After drilling, the given product had a 35% smaller volume than before. The hole's circumference in the base is equal to the height of the roller - Right circular cone
The volume of a right circular cone is 5 liters. The cone is divided by a plane parallel to the base, one-third down from the vertex to the base. Calculate the volume of these two parts of the cone. - 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. - Mountain and hiker
The hiker set out on a hike at 5 km/h. After 30 minutes, a cyclist on a mountain bike set off on the same route at 20 km/h. How many minutes will the cyclist overtake the tourist? - 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? - Material consumption
The sphere-shaped reservoir has a volume of 282 hl. Calculate the material consumption in m² for its production, assuming 8% for joints and waste, and round the final result to the nearest integers. - Triangle cone rotation
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 - Axial section
The axial section of the cylinder has a diagonal 50 cm. The shell size and base surface are in the ratio 2:5. Calculate the volume and surface area of this cylinder. - Roman 2
Roman thermae around the year 200 were baths equipped with underground central heating. The largest of them had a rectangular swimming pool with cold water, the bottom dimensions were 17m and 51m, the water reaches a height of 150 cm. Calculate according - Bricks pyramid
How many 50cm x 32cm x 30cm bricks are needed to build a 272m x 272m x 278m pyramid? - 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 - Ratio 52
The ratio of the surface area of a cube to its volume is 2:1.Calculate: a) the length of the edge of the cube in cm b) the volume of the cube in cm³ c) the volume of the cube in cm2 - Cuboid surface ratio
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. - Prism surface calculation
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. - Unknown metal
The prism made of unknown metal has dimensions of 3 cm by 3 cm by 5 cm and a weight of 121 g. What metal is it? Write its chemical symbol. - Alien ship
The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the large - Cube zoom
If we magnify the cube's edge by 47 %, how many percent does this increase the cube's volume and surface? - Vertical prism
The base of the vertical prism is a rhombus with diagonals of 24 cm and 10 cm. Suppose the shell area is 52% of the total surface area of the prism. Calculate its surface. - 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? - Sphere cube filling
Nine identical spheres are stacked in the cube to fill the cube's volume as much as possible. What part of the volume will the cube fill?
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