# Sphere + body volume - math problems

1. Kostka Kostka je vepsána do koule o poloměru r = 6 cm. Kolik procent tvoří objem kostky z objemu koule?
2. Wall thickness The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm3.
3. 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 paint is used for its double coat if you know that 1 kg of paint diluted with 1 deciliter of paint will paint an a
4. The ball The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger?
5. 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.
6. The hemisphere The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
7. Alien ship The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the large
8. Pebble The aquarium with internal dimensions of the bottom 40 cm × 35 cm and a height of 30 cm is filled with two-thirds of water. Calculate how many millimeters the water level in the aquarium rises by dipping a pebble-shaped sphere with a diameter of 18 cm.
9. Sphere VS Find the surface and volume of a sphere that has a radius of 2 dm. The radius of the sphere we reduce by 1/3 of the original radius. How much percent does the volume and surface of the sphere change?
11. Sphere floating Will float a hollow iron ball with an outer diameter d1 = 20cm and an inside diameter d2 = 19cm in the water? The iron density is 7.8 g/cm 3. (Instructions: Calculate the average sphere density and compare with the density of the water. )
12. Iron ball The iron ball has a weight of 100 kilograms. Calculate the volume, radius, and surface if the iron's density is h = 7.6g/cm3.
13. Volume of ball Find the volume of a volleyball that has a radius of 4 1/2 decimeters. Use 22/7 for π
14. Spherical tank The tank of a water tower is a sphere of radius 35ft. If the tank is filled to one quarter of full, what is the height of the water?
15. Cube into sphere The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
16. Hemispherical hollow The vessel hemispherical hollow is filled with water to a height of 10 cm =. How many liters of water are inside if the inside diameter of the hollow is d = 28cm?
17. Equilateral cylinder A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.
18. Inscribed Cube is inscribed in the cube. Determine its volume if the edge of the cube is 10 cm long.
19. Cube, cuboid, and sphere Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. In what ratio are the volumes of cube, cuboid, and sphere?
20. Inscribed sphere How many percents of the cube volume takes the sphere inscribed into it?

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