Solid geometry, stereometry - page 109 of 120
Number of problems found: 2399
- Submerged 81714
A concrete column with a density of 3500 kg/m3, a height of 6 m, and a square base of a=25 cm lies at the bottom of the dam at a depth of 10 m. At the upper end, it is lifted by a rope by a crane. 1) with how much force does the pole stretch th
- Diameter 3962
The diameter of the atomic nucleus is 10 to -12cm. How many atoms would fit on a 1 mm line if they could be arranged close together?
- Weigh 8301
How much does a gold cube weigh, 30 x 30 x 30 cm?
- Compressive 4894
At what depths does a hydrostatic compressive force of 3 kN act at a depth of 30 m in water?
- Cube zoom
If we magnify the cube's edge by 47 %, how many percent does this increase the cube's volume and surface?
- 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.
- 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.
- Bricks pyramid
How many 50cm x 32cm x 30cm bricks are needed to build a 272m x 272m x 278m pyramid?
- Tower roof
The tower's roof is a regular 4-sided pyramid with a height of 4m and an edge of the base of 6m. 25% of the roof covering was found to be damaged. How many square meters of coverage are needed to repair the roof?
- 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
- Bottles of juice
How many 2-liter bottles of juice need to buy if you want to transfer the juice to 50 pitchers' rotary cone shape with a diameter of 24 cm and a base side length of 1.5 dm?
- MO SK/CZ Z9–I–3
John had the ball that rolled into the pool and swam in the water. Its highest point was 2 cm above the surface. The circle's diameter that marked the water level on the ball's surface was 8 cm. Find the diameter of John's ball.
- 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?
- 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
- Lampshade
The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm² of material will we need when 10% is waste?
- Cylindrical tank
The cylinder-shaped tank with a diameter of 100 cm is 50% full and contains 7850 l of water. What is the height of the tank?
- Two cuboids
The cuboid has dimensions of 2m 3m 4m We increase the length of all edges by 50 cm. 1. Calculate in % how much the surface area of the cuboid increases compared to the surface area of the original cuboid - round the result to whole percent 2. Calculat
- Dimensions - crate
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
- 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?
- Original 63974
If we reduce the length of the cube edge by 30%, this cube has a reduced surface area of 1176 cm². Find the edge length and volume of the original cube.
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