Ratio + cube - practice problems
Number of problems found: 32
- Circumscribed 81025
A cube with a volume of 4096 cm³ is described and inscribed by a sphere. Calculate how many times the volume of the circumscribed sphere is greater than the inscribed sphere. - A cube
A cube has a surface area of 64 ft². Hedy creates a reduction of this cube using a scale factor of 0.5. What is the surface area of the reduction? - Material 65504
The cube with an edge of 1 cm weighs 0.2 kg. What is the weight of a cube made of the same material with an edge 4 cm long? - Identical 35961
Nine identical spheres are stacked in the cube to fill the volume of the cube as much as possible. What part of the volume will the cube fill?
- Geometric progression
If the 6th term of a GP is four and the 10th is 4/81, find common ratio r. - Distribute 32451
The king cannot decide how to distribute 4 cubes of pure gold, which have edges of length 3cm, 4cm, 5cm, and 6cm, to two sons as fairly as possible. Design a solution so that the cubes do not have to be cut. - Equilateral cone
We pour so much water into a container with the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down? - Cuboid and ratio
A cuboid has a volume of 810 cm³. The lengths of edges from the same vertex are in a ratio of 2:3:5. Find the dimensions of a cuboid. - Water container
The cube-shaped container is filled to two-thirds of its height. If we pour 18 liters, it will be filled to three-fifths of the height. What is the volume of the whole container?
- Determine: 10182
The lengths of the edges of two cubes are in the ratio 1:2, determine: a) the ratio of the content of the wall of the smaller cube to the content of the wall of the larger cube. b) the ratio of the surface of the smaller cube to the surface of the larger - Dimensions 7932
The volume of the block is 5760 cm³. For the dimensions of a given block, a: b = 4:3, b: c = 2:5 Calculate its surface. - 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. - Determine 7488
The lengths of the edges of the two cubes are in the ratio 2:3. Determine how many times the surface of the larger cube is larger than the surface of the smaller cube. - Seawater
Seawater density is 1025 kg/m³, and ice is 920 kg/m³. Eight liters of seawater froze and created a cube. Calculate the size of the cube edge.
- Cube, cuboid, and sphere
Volumes of a cube and a cuboid are in a ratio of 3:2. Volumes of a sphere and cuboid are in a ratio of 1:3. At what rate are the volumes of a cube, cuboid, and sphere? - Calculate 6275
A block with edges of lengths of 10 cm and 8 cm has the same volume as a cube with an edge of the length of 1 dm. Calculate the third dimension of the block. Compare the ratio of the surfaces of both bodies. - Length 6208
How does the volume of a cube change if we double the length of its edge? - 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 made, a cube. In what ratio are the surfaces of these cubes? - Cube edges
Find the cube edge length (in centimeters) that has a surface and volume expressed by the same numeric value. Draw this cube in a ratio of 1:2.
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