Solid geometry, stereometry - page 111 of 123
Number of problems found: 2442
- Pyramid roof
How many m² of the galvanized sheet is used to cover the roof of the tower, which has the shape of a four-sided pyramid, whose base edge is 6 m long? The height of the tower is 9 m. When covering, is 5% metal waste expected? - Cuboid Edges from Surface
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. - 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 6 cm, longer pendant 8 - 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 - Atomic diameter
The diameter of the atomic nucleus is 10 to -12 cm. How many atoms would fit on a 1 mm line if they could be arranged close together? - 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? - 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. After how many minutes will the cyclist overtake the hiker? - Gold Cube Weight
How much does a gold cube weigh, 30 x 30 x 30 cm? - Roof material calculation
How much sheet is needed for a roof with the shape of a regular quadrilateral pyramid if its edge is 2.8 m long and the height of the roof is 0.8 m? Calculate 10% for the overlap (extra). - 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. - Dimensions of a fabric
How many m² of fabric is needed to make a tent of a regular 3-sided prism if it is necessary to count on a 2% reserve of fabric? Dimensions - 2 m 1.6 m and height 1.4 m - 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? - Cube in sphere
The cube is inscribed in a sphere with a radius r = 6 cm. What percentage is the cube's volume from the ball's volume? - Cube zoom
If we magnify the cube's edge by 47 %, how many percent does this increase the cube's volume and surface? - 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. - Block surface ratio 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.
- Ratio of volumes
If the heights of two cylindrical drums are in the ratio 7:8 and their base radii are in the ratio 4:3. What is the ratio of their volumes? - Roman 2
Roman thermae around the year 200 AD were baths equipped with underground central heating. The largest of them had a rectangular pool of cold water with base dimensions of 17 m and 51 m, with the water reaching a height of 150 cm. Calculate according to P - Hydrostatic pressure
At what depths does a hydrostatic compressive force of 3 kN act at a depth of 30 m in water? - The coil
How many ropes (a diameter of 8 mm) fit on the coil (threads are wrapped close together)? The coil has the following dimensions: The inner diameter is 400 mm. The outside diameter is 800 mm. The length of the coil is 470 mm.
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