Solid geometry, stereometry - page 114 of 120
Number of problems found: 2399
- Truncated 43851
The pit is a regular truncated 4-sided pyramid, with 14 m and 10 m base edges and a depth of 6m. Calculate how much m³ of soil was removed when we dug this pit. - Average speed
What is the average speed you have to move around the world in 80 days? (Path along the equator, round to km/h). - Equator 6020
The Equator. ..40075 km train. ..300m. How many trains would fit on the Equator? - 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 - 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? - 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.
- Quadrilateral 5277
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. - Designated 44741
Cathedral height 110m, sphere weight 6000kg, dome diameter 43m, crane arm length 25m a) what was the diameter of this sphere? b) how much mechanical work had to be done to lift it to the designated place? - 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? - Cylinder-shaped part
A truncated cone-shaped part with base radii of 4 cm and 22 cm is to be recast into a cylinder-shaped part of the same height as the original part. What base radius will the new part have? - Hectoliters 4550
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 - 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%? - 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. - Semicircle 82687
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.
- Prescribed 4579
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. - 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? - Cylinder-shaped 12761
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 - Quadrilateral 71394
Sketch a grid of a quadrilateral prism with a rectangle of 1 cm x 3 cm and a height of 5 cm. - 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.
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