Solid geometry, stereometry - page 37 of 115
Solid geometry is the name for the geometry of three-dimensional Euclidean space.Stereometry involves the measurements of volumes of various solid figures (three-dimensional figures), including pyramids, prisms, and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres.
Number of problems found: 2283
- Measuring 67734
The candle has the shape of a block measuring 3 cm, 4 cm, and 5 cm. How many times is more wax used to make a candle if we gradually enlarge one, two, and all three edges twice? - Volume per time
The length of the cube-shaped tank edge is 4 m. A pump has a capacity of 200 l per minute. How long does fill take for a pump to fill a cube-shaped tank up to 75% of its height? - Completely 4226
The aquarium is shaped like a cube and is partially filled with water. For Peter, a cube with an edge of 8 cm fell into it and completely sank. The water level in the aquarium rose by 1 cm. What is the volume of the whole aquarium? - Sphere volume formula
If V=4/3 π r³, find the value of V when r = 7, the value of r when V=113 1/7
- Cube-shaped box
Find the size of the smallest possible cube-shaped box where three types of 3cm, 5cm, 6cm small cubes could be stacked to fully use the box space (each type of cube separately). Can you find out how many smallest cubes are in the box? - Identical cubes
From the smallest number of identical cubes whose edge length is expressed by a natural number, can we build a block with dimensions 12dm x 16dm x 20dm? - Millimeter 6629
The ice cube weighs 24g. Determine the size of its edge to the nearest millimeter. If the ice density is 917kg/m3 - Deformed 5992
Fifty small metal cubes with an edge length of 2 cm were deformed, and we made one large cube from this material. What is its surface? - Cube containers
Replace the two cube-shaped containers with 0.8 dm and 0.6 dm edges with a single cube-shaped one so that it has the same volume as the two original ones together. What is the length of the edge of this cube?
- Calculate 38073
1. Calculate the volume of a cube whose edge is 3.6 dm long. 2. Calculate the edge's size if you know its surface S = 2166 mm². - Magnified cube
If the lengths of the cube's edges are extended by 5 cm, its volume will increase by 485 cm³. Determine the surface of both the original and the magnified cube. - Tetrahedral prism
The height of a regular tetrahedral prism is three times greater than the length of the base edge. Calculate the length of the base edge if you know that the prism volume is 2187 cm³. - Volumes 7252
The block and the cube have the same volumes of 512 cm3, and the block has edge lengths of b = 6.4 cm and c = 10 cm. Can a cube and a block have the same edge length? - Cylinder container
If the cylinder-shaped container is filled with water to a height of 5 dm, it contains 62.8 hectoliters of water. Calculate the diameter of the bottom of the container. Use the value π = 3.14.
- Three cubes
Two cube-shaped boxes with edges a = 70 cm; b = 90 cm must be replaced by one cube-shaped box. What will be its edge? - Eight
Eight small Christmas balls with a radius of 1 cm have the same volume as one large Christmas ball. What has a bigger surface: eight small balls or one big ball? - Cuboid edges in ratio
Cuboid edge lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm³. - Iron sphere
Iron sphere has weight 100 kg and density ρ = 7600 kg/m³. Calculate the volume, surface, and diameter of the sphere. - Prism X
The prism with the edges of the lengths x cm, 2x cm, and 3x cm has a volume 29478 cm³. What is the area of the surface of the prism?
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