Hexagon rotation

A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?

Correct result:

V =  226.1947 cm3

Solution:

a=6 cm k=60/180=130.3333 h=a2(a/2)2=62(6/2)2=3 3 cm5.1962 cm S1=π h2=3.1416 5.1962284.823 cm2 V1=S1 a=84.823 6508.938 cm3 V2=1/3 S1 (a/2)=1/3 84.823 (6/2)84.823 cm3 V=k (V2+V1+V2)=0.3333 (84.823+508.938+84.823)=226.1947 cm3



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 2 comments:
#
Deepali.bhavale@gmail.com
Please specify the variables used ...using a figure will be great

#
Www
Body consist of 3 parts: cone + cylinder + cone.

avatar









Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • 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.
  • Quadrangular pyramid
    komoly Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the sidewall and the base plane.) S =? , V =?
  • Angle of diagonal
    hranol_9 Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
  • Octagonal pyramid
    octagonl_pyramid2 Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°.
  • Triangular pyramid
    TriangularPyramid What is the volume of a regular triangular pyramid with a side 3 cm long?
  • 4side pyramid
    ihlany Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
  • Tetrahedral pyramid
    pyramid_4s Calculate the regular tetrahedral pyramid's volume and surface if the content area of the base is 20 cm2, and the deviation angle of the side edges from the plane of the base is 60 degrees.
  • Hexagon cut pyramid
    truncated_hexa_pyramid Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm.
  • Square pyramid
    pyramid_4 Calculate the pyramid's volume with the side 5cm long and with a square base, side-base has an angle of 60 degrees.
  • Hexagonal pyramid
    hexagonal-pyramid The base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high.
  • Perimeter of triangle
    rt_triangle_1 In triangle ABC angle A is 60° angle B is 90° side size c is 15 cm. Calculate the triangle circumference.
  • 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.
  • Cone
    valec_8 The rotating cone volume is 9.42 cm3, with a height 10 cm. What angle is between the side of the cone and its base?
  • Hexagonal pyramid
    Hexagonal_pyramid Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm.
  • Hexagonal pyramid
    hexa_pyramid Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm.
  • Hexagonal pyramid
    hex_pyramid Please calculate the height of a regular hexagonal pyramid with a base edge of 5cm and a wall height of w = 20cm. Please sketch a picture.
  • Pyramid 8
    ihlan Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.