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.


k1 =  1.5
k2 =  1.5


Solution in text k1 =
Solution in text k2 =

Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!

Tip: Our volume units converter will help you with converion of volume units.

Next similar examples:

  1. Cylinder melted into cuboid
    cylinder_cube_3 A circular cylinder has area of cross section 56cm2 and the height is 10cm the cylinder is melted and made into a cuboid of base area 16cm2. What is the height of the cuboid?
  2. Pipes
    water_pipe Water pipe has a cross-section 1405 cm2. An hour has passed 756 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 15 hours if water flow same speed?
  3. Gutter
    okap How much metal is needed for production 46 pieces of gutter pipes with the diameter 12 cm and length of 4 m? The plate bends add 2% of the material.
  4. Lathe
    soustruh From the cube of edge 37 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?
  5. Axial section
    cylinder_cut Axial section of the cylinder has a diagonal 31 cm long and we know that the area of the side and the area of base is in ratio 3:2. Calculate the height and radius of the cylinder base.
  6. Axial section
    obr0 Axial section of the cylinder has a diagonal 40 cm. The size of the shell and the base surface are in the ratio 3:2. Calculate the volume and surface area of this cylinder.
  7. Velocity ratio
    rov_kontinuity Determine the ratio at which the fluid velocity in different parts of the pipeline (one part has a diameter of 5 cm and the other has a diameter of 3 cm), when you know that at every point of the liquid is the product of the area of tube [S] and the fluid.
  8. Lathe
    sustruh Calculate the percentage of waste if the cube with 53 cm long edge is lathed to cylinder with a maximum volume.
  9. Scale
    valec_vykres Cylinder was drawn in scale 2:1. How many times is the volume of the cylinder smaller in reality?
  10. Closed drum
    drum Find the total surface area of a closed cylindrical drum if it's diameter is 50 cm and height is 45 cm . (π= 3.14)
  11. Diameter of a cylinder
    cylinder_horiz_2 The diameter of the cylinder is 42 cm. How many times does the cylinder turn on a 66m long track?
  12. The painter
    painter_12 In order for the painter to get the desired color, he must mix green and yellow in a ratio of 4: 7. If it has 28 l of green color, how many liters of yellow color should he add? How many liters of mixed color does he get?
  13. Carrot seed
    mrkva2_1 Carrot seed germination is 85%, weight 1000 carrots seeds are 2.4g. How many seeds are likely to germinate if we sow 8g of seeds?
  14. A large
    two-gears A large gear will be used to turn a smaller gear. The large gear will make 75 revolutions per minute. The smaller gear must make 384 revolutions per minute. Find the smallest number of teeth each gear could have. [Hint: Use either GCF or LCM. ]
  15. Isosceles triangle
    iso_tr_1 In an isosceles triangle, the length of the arm and the length of the base are in ration 3 to 5. What is the length of the arm?
  16. Rectangular plot
    rectangular plot The dimensions of a rectangular plot are (x+1)m and (2x-y)m. If the sum of x and y is 3m and the perimeter of the plot is 36m. Find the area of the diagonal of the plot.
  17. Rectangular field
    rectangle_inside_circle_2 A rectangular field has a diagonal of length 169m. If the length and width are in the ratio 12:5. Find the dimensions of the field, the perimeter of the field and the area of the field.