# Cylinder + body volume - problems

1. 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.
2. An oil
An oil drum is cut in half. One half is used as a water trough. Use the dimensions; length 82cm, width 56cm to estimate the capacity of the water trough in liters.
3. The volume
The volume of a solid cylinder is 260 cm3 the cylinder is melt down into a cuboid, whose base is a square of 5cm, calculate the height of the cuboid and the surface area of the cuboid
4. Cylinders
Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much?
5. Lathe
From the cube of edge 37 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?
6. Floating barrel
Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.
7. Circular pool
The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?
8. Plastic pipe
Calculate weight of the plastic pipe with diameter d = 70 mm and length 380 cm if the wall thickness is 4 mm and the density of plastic is 1367 kg/m3.
9. Cylinder - basics
Cylinder with base radius r = 45 dm and height h=22 dm. Calculate:
10. The pot
The pot is in 1/3 filled with water. Bottom of the pot has an area of ​​329 cm2. How many centimeters rises water level in the pot after add 1.2 liters of water?
11. Gold wire
From one gram of gold was pulled wire 2.1 km length. What is it diameter if density of Au is ρ=19.5 g/cm3?
12. Hole
In the center of the cube with edge 14 cm we will drill cylinder shape hole. Volume of the hole must be 27% of the cube. What drill diameter should be chosen?
13. Cu wire
Copper wire has a length l = 980 m and diameter d = 8 mm. Calculate the weight if density of copper is ρ = 8500 kg/m3. Result round to one decimal place.
14. Cylinder
Calculate the dimensions of rotating cylindrical container with volume 2 l, if height of container is equal to the diameter of the base.
15. Cylinder - A&V
The cylinder has a volume 1287. The base has a radius 10. What is the area of surface of the cylinder?
16. Barrel 3
Barrel with water has a weight 118 kg. When we get off 75% of water it has a weight 35 kg. How many kg has empty barrel?
17. Cylinder - h
Cylinder volume is 163 cm3. Base radius is 10 cm. Calculate the height of the cylinder.
18. 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.
19. Lid
What is the weight of concrete cover (lid) to round shape well with a diameter 1.8 m, if the thickness of the cover is 11 cm? 1 m3 of concrete weighs 2190 kg.
20. Water container
Container with water weighs 1.48 kg. When we cast 75% of water container of water weight 0.73 kg. How heavy is an empty container?

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