Solid geometry, stereometry - page 110 of 121
Number of problems found: 2409
- Cuboid Edges from Surface
The edges of a cuboid are in the ratio 1:2:3. Calculate their length if you know that the surface of the entire cuboid is S=5632 m². Then, perform a test to ensure the calculation is correct. - Roof material calculation
How much sheet is needed for a roof with the shape of a regular quadrilateral pyramid if its edge is 2.8 m long and the height of the roof is 0.8 m? Calculate 10% for the overlap (extra). - Triangular prism
The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism. - Pyramid roof
How much m² of the galvanized sheet is used to cover the roof of the tower, which has the shape of a four-sided pyramid, whose base edge is 6 m long? The height of the tower is 9m. When covering, is 5% metal waste expected? - Block surface ratio The volume of the block is 7,500 dm³. The lengths of the edges are in the ratio 3: 4: 5. Calculate the surface area of the cuboid.
- Sphere and cone
Within the sphere of radius G = 33 cm, inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone? - Cube in sphere
The cube is inscribed in a sphere with a radius r = 6 cm. What percentage is the cube's volume from the ball's volume? - Iron ball
Calculate the radius of an iron ball with a density of 7.8g/cm³ and a mass of 7kg. - Pyramid stone weight
The largest Egyptian pyramid has the shape of a regular four-sided pyramid with a base edge of approximately 227 meters and a height of about 140 meters. How many tons of stone did the workers transport to build it? One cube of stone weighs 2500 kg and ne - Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base of 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure. - Dimensions of a fabric
How many m² of fabric is needed to make a tent of a regular 3-sided prism if it is necessary to count on a 2% reserve of fabric? Dimensions - 2m 1.6m and height 1.4m - Transforming cuboid
A cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length? - Ratio of volumes
If the heights of two cylindrical drums are in the ratio 7:8 and their base radii are in the ratio 4:3. What is the ratio of their volumes? - Perfect cubes
Suppose a number is chosen at random from the set (0,1,2,3,. .. ,202). What is the probability that the number is a perfect cube? - Metal balls
Four metal balls with a diameter of 5 cm are placed in a measuring cylinder with an inner diameter of 10 cm. What is the smallest water volume to be poured into the cylinder so that all balls are below the water level? - Cube painting
Entrepreneur Kostkoš wanted to produce colorful blocks for schools. But he gave them to another businessman to paint, who asked €1,117.2 for painting 1,000 cubes. The area that needs to be painted on one cube is 294 square centimeters. Please write how ma - The coil
How many ropes (a diameter of 8 mm) fit on the coil (threads are wrapped close together)? The coil has the following dimensions: The inner diameter is 400mm. The outside diameter is 800mm. The length of the coil is 470mm. - Cone cutout
The cone shell with a base radius of 20 cm and a height of 50 cm unfolds into a circular cutout. How big is the center angle of this cutout? - Air mass
What is the weight of the air in a classroom with dimensions 10 m × 3 m × 3 m? The air density is 1.293 kg/m³. - Similarity
Rectangle ABCD has dimensions of 7 cm and 8 cm. Rectangle PQRS has dimensions 7 cm and 6 cm. Determine the coefficient of the similarity k of the rectangles; if they aren't similar, enter zero as the coefficient of similarity.
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