Solid geometry, stereometry - page 116 of 123
Number of problems found: 2442
- 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. - Cone projection
In axonometry, construct a projection of an oblique circular cone with a base in a plane. The stop triangle gives dimension. We know the center of the base S, the radius of the base ra the top of the cone V, Triangle (6,7,6), S (2,0,4), V (-2,7,6), r = 3 - Trains on Equator
The Equator. ..40075 km train. ..300 m. How many trains would fit on the Equator? - Megapascals
What is the area of cross-section of the piston if the force of 300 kN produces a pressure of 5 MPa? - Pyramid soil
The pit is a regular truncated 4-sided pyramid, with 14 m and 10 m base edges and a depth of 6 m. Calculate how much m³ of soil was removed when we dug this pit. - Gold wire
A wire of length 1.4 km was drawn from one gram of gold. What is its diameter if the density of gold is ρ = 19.5 g/cm³? - Prism Box Force Weight
We turn the prism-shaped box with a height of 1 m and a square base with an edge of 0.6 m under a force of 350 N, which acts horizontally compared to the upper edge. What is the weight of the box? - 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. - Pillar
Calculate the volume of a pillar in the shape of a regular quadrilateral frustum (truncated pyramid) with base edges a = 10 and b = 19, and height h = 28. - 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? - Candles
Before Christmas, Eve 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 - 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. - 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? - 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? - 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. - 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. - Ice and water
We want to cover a rectangular rink with dimensions of 55 m and 25 m with a 4 cm thick layer of ice. How many liters of water do we need if freezing water increases its volume by 10%? - 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? - 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 - 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?
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