Truncated cone

Calculate the height of the rotating truncated cone with volume V = 1115 cm3 and a base radii r1 = 7.9 cm and r2 = 9.7 cm.

Result

h =  4.57 cm

Solution:

Solution in text h =







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

Showing 5 comments:
#
Math student
can u explain why you do (r2 + rxR + R2) in the first step

5 months ago  3 Likes
#
Dr Math
Fine math problem! Go ahead!

#
Kukoslav
but to prove formula, you need to know how to solve integral

#
Kukoslav
need to solve a cubic equation, as obtained above, to find rises in heights... integral

avatar









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

Next similar examples:

  1. Rotating cone II
    cone Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
  2. Cone
    truncated_cone_1 Circular cone with height h = 29 dm and base radius r = 3 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume.
  3. 2x cone
    truncated_cone_2 Circular cone height 84 cm was cut plane parallel with base. Volume of these two small cones is the same. Calculate the height of the smaller cone.
  4. Rotary cone
    cone_2 Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm3. Calculate the radius of the base circle and height of the cone.
  5. Cone and the ratio
    kuzel Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
  6. Angle of deviation
    kuzel2_1 The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
  7. Rotation
    cone_1 Right triangle with legs 14 cm and 20 cm rotate around longer leg. Calculate the volume and surface area of the formed cone.
  8. Cut and cone
    kuzel Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
  9. Axial section
    cone2 Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
  10. Cone A2V
    popcorn Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
  11. Cone
    cone-blue Calculate volume and surface area of ​​the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°.
  12. Rotary cone
    cone_3 The volume of the rotation of the cone is 472 cm3 and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone.
  13. Canopy
    cone-roof Mr Peter has metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 3.3 m2?
  14. Sandpile
    sandpile_1 Auto sprinkled with sand to an approximately conical shape. Workers wanted to determine the volume (amount of sand) and therefore measure the circumference of the base and the length of both sides of the cone (over the top). What is the volume of the san
  15. Tower
    cone_roof How many m2 of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°?
  16. The cone
    cone_5 The lateral surface area of the cone is 4 cm2, the area of the base of the cone is 2 cm2. Determine the angle in degrees (deviation) of the cone sine and the cone base plane. (Cone side is the segment joining the vertex cone with any point of the base ci
  17. Cone
    cones_1 If the segment of the line y = -3x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone?