Practice problems of the prism - last page
A prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases. Prisms are named for their bases, so a prism with a pentagonal base is called a pentagonal prism.Number of problems found: 520
- Cubes into cuboid
How many 12-centimeter cubes fit into the block (cuboid) with 6 dm, 8.4dm, and 4.8? - Pine wood
We cut a carved beam from a trunk of pine 6 m long and 35 cm in diameter. The beam has a cross-section in the shape of a square. The square has the greatest area. Calculate the length of the sides of a square. Calculate the volume in cubic meters of lumbe - The square
The square oak board (with density ρ = 700 kg/m3) has a side length of 50 cm and a thickness of 30 mm. 4 holes with a diameter of 40 mm are drilled into the board. What is the weight of the board? - Calculate 26051
The base of the prism has the shape of a square with a side of 10 cm. The height of the prism is 20 cm. Calculate the height of a pyramid with a square base of 10 cm, which has four times the prism's volume.
- Regular square prism
The volume of a regular square prism is 192 cm³. The size of its base edge and the body height is 1:3. Calculate the surface of the prism. - Cylinder-shaped 4411
A cylinder-shaped hole with a diameter of 12 cm is drilled into a block of height 50 cm with a square base with an edge length of 20 cm. The axis of this opening passes through the center of the base of the cuboid. Calculate the volume and surface area of - Max - cone
The workshop must produce the greatest cone from the iron bar (shape = prism) with dimensions 6.2 cm, 10 cm, and 6.2 cm. a) Calculate cone volume. b) Calculate the waste. - Rectangle pool
Find dimensions of an open pool with a square bottom with a capacity of 32 m³ to have painted/bricked walls with the least amount of material. - Cylindrical 83193
How much concrete is needed to pour 8 concrete columns with a square base: a = 38 cm, the height of the columns being 6.2 m? Each column has a cylindrical cavity with a diameter of 15 cm.
- Cube-shaped 81023
The cube-shaped pool is 50 m long and 16 m wide. They poured 12,000 hl of water into it. Calculate the surface area of the pool that is wetted by water. - Quadrangular 64564
The surface of the quadrangular block is 3.4 dm². The edges of the figure are 8cm and 10cm long. Calculate the volume of the prism. - 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. - Prism
Three cubes are glued into a prism. The sum of the lengths of all its edges is 115 cm. What is the length of one edge of the original cube? - Cylinder horizontally
The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the cylinder's axis. How many hectoliters of water is in the cylinder?
- Cylindrical 7891
Is it possible to pour water from a full cube-shaped container measuring 8 cm, 10 cm, and 12 cm into a cylindrical container with a bottom diameter of 12 cm and a height of 8 cm? - Circumference 81557
Calculate how many volleyballs with a circumference of 65 cm fit into a cube-shaped rack whose edge is 100 cm long. - Rainwater 83296
What volume must a cylinder-shaped tank have to collect rainwater from the flat roof of a cube-shaped house if the house is 12m wide and reports 50mm of rainfall? - 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 - Dimensions: 32561
The convex lens consists of two spherical segments (dimensions given in mm). Calculate its weight if the density of the glass is 2.5 g/cm³. Dimensions: 60mm in length and width of the upper part 5mm, the width of the lower part 8mm
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