Solid geometry, stereometry - page 96 of 121
Number of problems found: 2418
- Cone and cube
About what percentage has cone with base radius r larger volume than a same high cube with square base with edge length r? - Wall brick count
How many bricks are needed to build a wall that is 12 m long, 1.6 m high, and 47 cm wide if the dimensions of the brick are 30 x 15 x 7.5 cm and 5% of the wall volume is mortar? - Surface of cubes
Peter molded a cuboid of 2 cm, 4cm, and 9cm of plasticine. Then, the plasticine was split into two parts in a ratio of 1:8. From each piece, a cube was made. In what ratio are the surfaces of these cubes? - Cuboid - ratios
The sizes of the edges of the cuboid are in the ratio of 2:3:5. The smallest wall has an area of 54 cm². Calculate the surface area and volume of this cuboid. - Gold ring
A gold ring with a width of 1 cm is made by drilling a sphere with a radius of 1 cm through its center. A gold bracelet with a width of 1 cm is made by drilling a sphere with a radius of 4 cm through its center. Which piece of jewelry will be worth more i - Barrel of oil
The barrel of oil weighs 283 kg. When it molded 26% oil, it weighed 216 kg. What is the mass of the empty barrel? - Cone in cube
The cube is an inscribed cone. Determine the ratio of the volume of the cone and cube. Please write the ratio as a decimal number and as a percentage. - Ice Cream Cones Volume
How many cone-shaped cones will we have to take to fill 20 l of creams (to the brim) if the cone has an inner base diameter of 6 cm and a height of 8 cm. Make a drawing, and write the answer. - Sphere cut
A sphere segment is cut off from a sphere k with radius r = 1. The volume of the sphere inscribed in this segment is equal to 1/6 of the segment's volume. What is the distance of the cutting plane from the center of the sphere? - Safe wall percentage
The safe is 100 cm high, 80 cm wide, and 60 cm deep. Its internal space has a volume of 168 liters. What percentage of the total volume of the safe is occupied by the walls of the safe? - Block dimension ratio
The block's dimensions are 9:5:4. Determine its volume if you know that the sum of the longest and shortest edges is 65 cm. - Five-sevenths of a volume
Forty-two liters of water fill the barrel to two-thirds of its volume. If it is filled to five-sevenths of a volume, how many liters of water do we need to add? - How many 9
How much percent volume remains of a sphere if the diameter decrease 3×? - No smoke
Tobacco company NO-SMOKE adorned its stand at the cigarette-type trade fair with cigarette-shaped. The dimensions of which were 20 times the size of a regular cigarette. Regular cigarette contains 0.8 mg of nicotine. How much nicotine would a giant cigare - Cube face coloring
We painted a wooden cube with an edge 4 cm long with green paint over the entire surface. Then we cut it into small cubes with an edge length of 1 cm. The number of cubes that have precisely two faces colored green is: - Percentage - prism and cube
Prism with square base a=25cm, height h=45cm. cube: b=15cm a) what percentage of the volume of the prism is the volume of the cube? b) what height should the prism have to have the same volume as the cube? - Hole
We will drill the cylinder shape hole in the cube's center with an edge 16 cm. The volume of the hole must be 10% of the cube. What should drill diameter be chosen? - Cone
The circular cone has height h = 15 dm and base radius r = 2 dm slice plane parallel to the base. Calculate the distance of the cone vertex from this plane if solids have the same volume. - Cuboid - ratio
Find the volume of a block whose dimensions are in the ratio 2:3:4 and the surface is 117 dm². - Cube cuboid minimum
Let us have a cube whose edge length is expressed in centimeters and is a natural number. What is the smallest number of such identical cubes that can be made into a cuboid with dimensions of 24 cm, 32 cm, and 60 cm? How long will the edge of these cubes
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