Solid geometry, stereometry - page 112 of 121
Number of problems found: 2409
- Slant surface
The surface of the rotating cone and its base area is in the ratio 18:5. Determine the volume of the cone if its body height is 12 cm. - Tower
Charles built a tower of cubes with an edge 2 cm long. In the lowest layer, there were six cubes (in one row) in six rows. In each subsequent layer, always one cube and one row less. What volume in cm³ did the whole tower have? - Rope
How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and a length of 350 mm (the central mandrel has a diameter of 50 mm)? - Fe vs. H2O
The volume of what the body of the same weight is greater: iron or water? - Two cubes 3
Two cubes modeled from plasticine have single-digit integer edge lengths with a difference of 1 cm. Can one large cube with an integer edge length be modeled from the same amount of plasticine? - Two pots
Two similar pots have 16 cm and 10 cm heights if the smaller pot holds 0,75 l. Find the capacity of the larger pot - Cylinder surface
The area of the rotating cylinder shell is half the area of its surface. Calculate the surface of the cylinder if you know that the diagonal of the axial section is 5 cm. - Volume and surface
Calculate the volume and surface area of the cylinder when the cylinder height and base diameter are in a ratio of 3:4, and the area of Lateral Surface Area (LSA) is 24 dm². - Cone and the ratio
The rotational cone has a height of 59 cm, and the ratio of the base surface to the lateral surface is 10: 12. Calculate the surface of the base and the lateral surface. - 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. - Cube Edge from Surface
Determine the length of the edge of the cube, the surface of which is equal to 60% of the surface of a block measuring 7cm, 8cm, 6cm - Rectangle pool
Find the dimensions of an open pool with a square bottom and a capacity of 32 m³ that can have painted/bricked walls with the least amount of material. - Cuboid and ratio
A cuboid has dimensions in a ratio of 1:2:6, and the surface area of the cuboid is 1000 dm². Calculate the volume of the cuboid. - Centimeters - block
The surface of the block is 4596 square centimeters. Its sides are in a ratio of 2:5:4. Calculate the volume of this block. - Iron bar weight
Calculate the weight of an iron bar 1.2 m long, whose cross-section is a trapezoid with dimensions a=10 cm c=8 cm and the distance between the bases v=6 cm. As we know, 1 cubic meter of iron weighs 7800 kg. - A cube
A cube has a surface area of 64 ft². Henrietta creates a reduction of this cube using a scale factor of 0.5. What is the surface area of the reduction? - Ladder
A 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall? - Copper winding
Calculate the current flowing through the copper winding at an operating temperature of 70°C Celsius if the winding diameter is 1.128 mm and the coiled length is 40 m. The winding is connected to 8V. - Block volume ratio
The block surface is 5,632 m². The lengths of the edges are in the ratio 1: 2 : 3. Calculate the volume of the cuboid. - Conical area
A right-angled triangle has sides a=12 and b=19 at the right angle. The hypotenuse is c. If the triangle rotates on the c side as an axis, find the volume and surface area of the conical area created by this rotation.
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