Solid geometry + reason - practice problems - page 2 of 4
Number of problems found: 63
- Precisely 64114
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: - Centimeters 4178
Find the surface of a block whose one wall is 48 centimeters square and the other wall is 30 centimeters square. - Centimeters 82756
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 - Circumference 81557
Calculate how many volleyballs with a circumference of 65 cm fit into a cube-shaped rack whose edge is 100 cm long.
- Into box
How many cubes with an edge of 2.5 cm fit into a box measuring 11.6 cm, 8.9 cm, and 13.75 cm? - Hexagon rotation
A regular hexagon of side 6 cm is rotated at 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated? - Opposite 79954
We color a wooden cube with an edge length of 3 cm so that three walls are blue, three are red, and no two opposite walls are the same color. Cut the cube into 1 cm³ cubes. How many cats will have at least one red wall and at least one blue wall? - Spheres in sphere
How many spheres with a radius of 15 cm can fit into the larger sphere with a radius of 150 cm? - Theoretically 35321
Calculate how many soccer balls (the volume of one is 7,200 cm3) theoretically fit into a room with dimensions of 8x5x3 m. Neglect the gaps between the balls.
- A cylinder
A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly six complete turns around the cylinder while its two ends touch the top and bottom. (forming a spiral around the cylinder). How long is the string in cm? - Billiard balls
A layer of ivory billiard balls radius of 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to everyone adjacent to it. In the spaces between sets of 4 adjacent balls, other balls rest, equal in size to the original. - Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in the corner of a room. The spheres are each tangent to the walls and floor an - Painting
To paint the pool with dimensions: 2 meters depth, 3m x 4m we bought paint to 50 meters square. How much "paint" will be wasted? - Ribbon on the cube
A cubical gift box is tied with a piece of ribbon. If the total length of the free ends and the bow is 18 inches, what is the length of the ribbon used? (Each side of the cube is 6 inches).
- The body
The body on the figure consists of cubes with an edge length of 10 cm. What surface has this body? - Determine 8010
Determine the cone's base's radius if its shell develops into a circular section with radius "s" = 10 and center angle x = 60 °. r = ?, o =? - Dimensions 81670
A wooden crate with dimensions d=3m, e=4m, and f=3m was placed in a transport container with dimensions a=10 m, b=4m, and c=3m. What is the maximum length of a straight, rigid rod of negligible diameter that can still be placed in the container in this si - Calculate 19543
Calculate the surface of a prism with a square base whose mantle is a rectangle with sides of 18cm and 8cm. How many solutions does the task have? List all solutions. - Tetrahedron 83144
A container shaped like a rotating cylinder with a base radius of 5 cm is filled with water. If a regular tetrahedron with an edge of 7 cm is immersed in it, how much will the water level in the container rise?
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