Solid geometry, stereometry - page 110 of 121
Number of problems found: 2404
- Compressive 4894
At what depths does a hydrostatic compressive force of 3 kN act at a depth of 30 m in water? - Quadrilateral 29201
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). - 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? - Alien ship
The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the large - Cube zoom
If we magnify the cube's edge by 47 %, how many percent does this increase the cube's volume and surface? - Identical 35961
Nine identical spheres are stacked in the cube to fill the cube's volume as much as possible. What part of the volume will the cube fill? - 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. - Weight of air
What is the weight of air in the living room measuring width 6 m, length 4 m, and height 2.56 m? Air density is ρ = 1.2959 kg/m³. - Rectangle pool
Find the dimensions of an open pool with a square bottom and a capacity of 32 m³ that can have painted/bricked walls with the least amount of material. - 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? - 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. - Two bodies
The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Find the ratio of surfaces of the first and second bo - 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 - Conical area
A right-angled triangle has sides a=12 and b=19 at the right angle. The hypotenuse is c. If the triangle rotates on the c side as an axis, find the volume and surface area of the conical area created by this rotation. - Unknown metal
The prism made of unknown metal has dimensions of 3 cm by 3 cm by 5 cm and a weight of 121 g. What metal is it? Write its chemical symbol. - Entrepreneur 4367
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 - Material consumption
The sphere-shaped reservoir has a volume of 282 hl. Calculate the material consumption in m² for its production, assuming 8% for joints and waste, and round the final result to the nearest integers. - Rope
How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and a length of 350 mm (the central mandrel has a diameter of 50 mm)? - Axial section
The axial section of the cylinder has a diagonal 50 cm. The shell size and base surface are in the ratio 2:5. Calculate the volume and surface area of this cylinder. - Circular 4690
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?
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