Solid geometry, stereometry - page 115 of 121
Number of problems found: 2409
- Quadrilateral 71394
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? - 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? - 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 4cm thick layer of ice. How many liters of water do we need if freezing water increases its volume by 10%? - 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. - 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 - 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? - 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? - 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? - 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? - 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? - 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. - 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? - 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 2.8 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. - Soap bubble
A conductive soap bubble with a radius of r=2 cm and charged to a potential of φ= 10000 V will burst into a drop of water with a radius of r1= 0.05 cm. What is the potential φ1 of the drop? - 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? - Scale
The student drew the cylinder in scale 7:1. How many times is the volume of the cylinder smaller in reality?
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