Solid geometry, stereometry - page 115 of 120
Number of problems found: 2399
- Fuel economy
How many kilometers is sufficient petrol in the cylinder fuel tank with a diameter of 40 cm and the base of tank length of 1 m when it is filled to 60%, and if the car consumes 15 liters per 100 km? - Measuring cork
Simon boasted that he had taken away a block of cork measuring 0.5m x 0.5m x 1.2m. Is it possible we know that 1 m of cubic cork weighs 300 kg and children from 10 to 15 years old can carry a maximum load of 5 kg? - Through 82036
5 m³ of water flows through the pipe in 1 second at a maximum speed of 2 m/s. What is the pipe radius? - Distribute 32451
The king cannot decide how to distribute 4 cubes of pure gold, which have edges of length 3cm, 4cm, 5cm, and 6cm, to two sons as fairly as possible. Design a solution so that the cubes do not have to be cut. - North Pole
What is the shortest distance across the globe's surface on a scale of 1:1,000,000 from the equator to the North Pole? - Perpendicular 5865
We cut the cube with two mutually perpendicular cuts, each parallel to one of the cube's walls. By what percentage is the sum of the surfaces of all cuboids created in this way greater than the surface of the original cube? - Eiffel Tower
The Eiffel Tower in Paris is 300 meters high and made of steel. It weighs 8,000 tons. If the tower model made of the same material weighs 1.8 kg, how tall is it?
- Seawater
Seawater density is 1025 kg/m³, and ice is 920 kg/m³. Eight liters of seawater froze and created a cube. Calculate the size of the cube edge. - Ice rink
A rectangular rink measuring 15m and 20m long needs to be covered with a layer of ice 4.5cm high. How many liters of water are needed to create ice? - Pipes
The water pipe has a cross-section 1903 cm². An hour has passed 859 m³ of water. How much water flows through the pipe with cross-section 300 cm² per 11 hours if water flows at the same speed? - Velocity ratio
Determine the ratio at which the fluid velocity in different parts of the pipeline (one piece has a diameter of 5 cm and the other has a diameter of 3 cm) when you know that every point of the liquid is the product of the area of the tube [S] and the flui - Dice - 5 times
We roll the dice five times. Make sentences: a) 3 events that definitely cannot happen. Write a reason for each. b) 3 events that will definitely occur; write a reason for each. Another problem: 3 events that may or may not occur for each. Write a reason. - Ice + water
A rectangular ice rink measuring 60 m by 30 m had a layer of ice 3 cm high. How many liters of water were used to create the ice? - Equilateral cylinder
A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere. - Sphere floating
Will a hollow iron ball float with an outer diameter of d1 = 20cm and an inside diameter of d2 = 19cm in the water? The iron density is 7.8 g/cm³. (Instructions: Calculate the average sphere density and compare it with the water density. )
- Shortest walk
An ant is crawling around this cube. The cube is made of wire. Each side of the cube is 3 inches long. (Those sides are called edges.) Points A and B are vertices of the cube. What is the least distance the ant would have to crawl if it starts from point - Octahedron - sum
On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7, and 8, wherein on different sides are different numbers. John makes the sum of the numbers written on three adjacent walls for each wall. Thus got eight sums, which al - Scale
The student drew the cylinder in scale 7:1. How many times is the volume of the cylinder smaller in reality? - Water channel
The cross-section of the water channel is a trapezoid. The bottom width is 19.7 m, the water surface width is 28.5 m, and the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flows - Cuboids
Two separate cuboids with different orientations are in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
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