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 very happy if you find an error in the example, spelling mistakes, or inaccuracies, and please send it to us. We 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:

  • Regular hexagonal pyramid
    hexa_pyramid Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height of w = 20cm. Sketch a picture.
  • Wall height
    hexa_pyramid Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height w = 20 cm.
  • 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.
  • Five-gon
    5gon_diagonal Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.
  • Pentagonal pyramid
    pyramid-pentagon Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 7.7 cm and a plane ABV, ABC has angle 37 degrees.
  • Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 4 cm.
  • Candy - MO
    cukriky_4 Gretel deploys to the vertex of a regular octagon different numbers from one to eight candy. Peter can then choose which three piles of candy give Gretel others retain. The only requirement is that the three piles lie at the vertices of an isosceles trian
  • Right angle
    triangles_1 If a, b and c are two sides of a triangle ABC, a right angle in A, find the value on each missing side. If b=10, c=6
  • RT - inscribed circle
    rt_incircle In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
  • Right triangles
    PT How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget to the triangle inequality).
  • Reference angle
    anglemeter Find the reference angle of each angle:
  • Annulus
    annulus_inscribed_circles Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n.
  • Two parallel chords
    chords_equall The two parallel chords of the circle have the same length of 6 cm and are 8 cm apart. Calculate the radius of the circle.
  • Vertices of RT
    RightTriangleMidpoint_3 Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
  • RT and circles
    r_triangle Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.
  • Right 24
    euclid_theorem Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you.
  • Isosceles IV
    iso_triangle In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.