Solid geometry, stereometry - page 115 of 121
Number of problems found: 2418
- Pyramid intersection
Given a regular quadrilateral pyramid ABCDV, point M is inside its edge AV, and point N is on the long line DC beyond point C. Construct the intersection of the plane MNV with the plane BCV and the intersection of the line MN and the plane BCV. - Gold wire
From one gram of gold was pulled wire 1.4 km length. What is its diameter if the density of Au is ρ=19.5 g/cm³? - Cone semicircle proof
If the shell of a cone is a semicircle, then the diameter of the cone's base is equal to its side's length. Prove it. - Megapascals
What is the area of cross-section of the piston if the force of 300 kN produces a pressure of 5 MPa? - Pillar
Calculate the volume of the pillar shape of a regular tetrahedral truncated pyramid if his square has sides a = 10, b = 19, and height is h = 28. - Prism grid sketch
Sketch a grid of a quadrilateral prism with a rectangle of 1 cm x 3 cm and a height of 5 cm. - Cathedral roof sphere
Cathedral height is 110 m, sphere weight 6000 kg, dome diameter 43 m, crane arm length 25 m a) what was the diameter of this sphere? b) how much mechanical work had to be done to lift it to the designated place? - Octagonal pyramid
Draw an octagonal pyramid in free parallel projection if the length of the edge a = 3 cm and the height of the pyramid v = 6 cm. - Water level increase
During the experiment, water flows evenly into a cylinder-shaped container. At the end of the 5th minute of the experiment, the water level was 25% higher than at the beginning of the experiment. 0 how many percent higher will the water level be at the en - The projection
In axonometry, construct the projection of a perpendicular 4-sided pyramid with a square base ABCD in the plane. The base triangle gives the axonometry. We know the center of the base S, the point of the base A, and the height of the pyramid v. - Candles
Before Christmas, Eva bought two cylindrical candles—red and green. Red was 1 cm longer than green. She lit a red candle on Christmas Day at 5:30 PM and a green candle at 7:00 PM, leaving them on fire until they burned. At 9:30 PM, both candles were the s - Pipe water radius
5 m³ of water flows through the pipe in 1 second at a maximum speed of 2 m/s. What is the pipe radius? - Icerink
A rectangular rink with 68.7 m and 561 dm dimensions must be covered with a layer of ice 4.2 cm thick. How many liters of water is necessary for ice formation when the ice volume is 9.7% greater than the volume of water? - Pool volume
The water's surface in the pool is a rectangle 50 meters long and 12 meters wide. The water depth rises evenly from 1 meter at one end of the pool to 3 meters at the other end of the pool (longer sides). Determine the amount of water in the pool in hectol - 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? - Ice and water
We want to cover a rectangular rink with dimensions of 55 m and 25 m with a 4cm thick layer of ice. How many liters of water do we need if freezing water increases its volume by 10%? - Freezer
The freezer has the shape of a cuboid with internal dimensions of 12 cm, 10 cm, and 30 cm. A layer of ice 23 mm thick was formed on the freezer's inner walls (and on the opening). How many liters of water will drain if we dispose of the freezer? - 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? - Ball diameter
The racing ball for men has a prescribed weight of 7250g. It is made of iron. How does its diameter change if we make it from lead? The density of iron is 7.8 g / cm cubic, and the density of lead is 11.3 t / m cubic. - 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?
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