# 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?

Result

V =  226.195 cm3

#### Solution:

$a=6 \ \text{cm} \ \\ k=60/180=\dfrac{ 1 }{ 3 } \doteq 0.3333 \ \\ h=\sqrt{ a^2-(a/2)^2 }=\sqrt{ 6^2-(6/2)^2 } \doteq 3 \ \sqrt{ 3 } \ \text{cm} \doteq 5.1962 \ \text{cm} \ \\ S_{1}=\pi \cdot \ h^2=3.1416 \cdot \ 5.1962^2 \doteq 84.823 \ \text{cm}^2 \ \\ V_{1}=S_{1} \cdot \ a=84.823 \cdot \ 6 \doteq 508.938 \ \text{cm}^3 \ \\ V_{2}=1/3 \cdot \ S_{1} \cdot \ (a/2)=1/3 \cdot \ 84.823 \cdot \ (6/2) \doteq 84.823 \ \text{cm}^3 \ \\ V=k \cdot \ (V_{2}+V_{1}+V_{2})=0.3333 \cdot \ (84.823+508.938+84.823) \doteq 226.1947 \doteq 226.195 \ \text{cm}^3$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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

Showing 2 comments:
Please specify the variables used ...using a figure will be great

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

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

## Next similar math problems:

1. Wall height
Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height w = 20 cm.
2. Regular hexagonal 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.
3. Cut and cone
Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
4. Five-gon
Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.
5. Tetrahedron
Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
6. Candy - MO
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 triang
7. 4s pyramid
Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?
8. Truncated cone 5
The height of a cone 7 cm and the length of side is 10 cm and the lower radius is 3cm. What could the possible answer for the upper radius of truncated cone?
9. Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
10. Right triangles
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).
11. Circle
On the circle k with diameter |MN| = 61 J lies point J. Line |MJ|=22. Calculate the length of a segment JN.
12. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
13. The fence
I'm building a fence. Late is rounded up in semicircle. The tops of late in the field between the columns are to copy an imaginary circle. The tip of the first and last lath in the field is a circle whose radius is unknown. The length of the circle chord
14. Annulus
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.
15. Is right triangle
Decide if the triangle XYZ is rectangular: x = 4 m, y = 6 m, z = 4 m
16. Right 24
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.
17. Triangle IRT
In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB.