Number of problems found: 111
- The observatory
The dome of the hemisphere-shaped observatory is 5.4 meters high. How many square meters of sheet metal needs to be covered to cover it, and 15 percent must be added to the minimum amount due to joints and waste?
- Tropics and polar zones
What percentage of the Earth’s surface lies in the tropical, temperate and polar zone? Individual zones are bordered by tropics 23°27' and polar circles 66°33'
- Two balls
Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
- What is bigger?
Which ball has a larger volume: a football with a circumference of 66 cm or a volleyball with a diameter of 20 cm?
- The prison ball
Calculate the density of the material that the prison ball is made from if you know its diameter is 15cm and its weight is approximately 2.3kg. With the help of mathematical-physicochemical tables estimate what material the ball is made from.
Ping pong balls have a diameter of approximately 5.1 cm. It sold in boxes of 10 pieces: each box has a cuboid shape with a square base. The balls touch the walls of the box. Calculate what portion of the internal volume of the box is filled with balls.
- Float boya
A 0.5 meter spherical float is used as a location mark for a fishing boat anchor. It floats in salt water. Find the depth to which the float sinks if the material of which the float is made weighs 8 kilograms per cubic meter and salt water weighs 1027 kg/
- Hemisphere - roof
The shape of the observatory dome is close to the hemisphere. Its outer diameter is 11 m. How many kilograms of paint and how many liters of thinner is used for its double coat if you know that 1 kg of paint diluted with 1 deciliter of thinner will paint
- Plasticine ball
Plasticine balls have radius r1=85 cm, r2=60 mm, r3=59 cm, r4=86 cm, r5=20 cm, r6=76 mm, r7=81 mm, r8=25 mm, r9=19 mm, r10=14 cm. For these balls
- MO SK/CZ Z9–I–3
John had the ball that rolled into the pool, and it swam in the water. Its highest point was 2 cm above the surface. The diameter of the circle that marked the water level on the surface of the ball was 8 cm. Find the diameter of John ball.
- Billiard balls
A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original.
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