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.

Result

V =  38.971 cm3
S =  74.095 cm2

Solution:

a=3 cm h=5 cm S1=3⋅ 3/2⋅ a2=3⋅ 3/2⋅ 32≐23.3827 cm2 V=S1⋅ h/3=23.3827⋅ 5/3≐38.9711≐38.971 cm3a=3 \ \text{cm} \ \\ h=5 \ \text{cm} \ \\ S_{1}=3 \cdot \ \sqrt{ 3 }/2 \cdot \ a^2=3 \cdot \ \sqrt{ 3 }/2 \cdot \ 3^2 \doteq 23.3827 \ \text{cm}^2 \ \\ V=S_{1} \cdot \ h/3=23.3827 \cdot \ 5/3 \doteq 38.9711 \doteq 38.971 \ \text{cm}^3
a2=3/2⋅ a=3/2⋅ 3≐2.5981 cm h2=a22+h2=2.59812+52≐5.6347 cm S2=a⋅ h2/2=3⋅ 5.6347/2≐8.4521 cm2 S=S1+6⋅ S2=23.3827+6⋅ 8.4521≐74.0951≐74.095 cm2a_{2}=\sqrt{ 3 }/2 \cdot \ a=\sqrt{ 3 }/2 \cdot \ 3 \doteq 2.5981 \ \text{cm} \ \\ h_{2}=\sqrt{ a_{2}^2+h^2 }=\sqrt{ 2.5981^2+5^2 } \doteq 5.6347 \ \text{cm} \ \\ S_{2}=a \cdot \ h_{2}/2=3 \cdot \ 5.6347/2 \doteq 8.4521 \ \text{cm}^2 \ \\ S=S_{1}+6 \cdot \ S_{2}=23.3827+6 \cdot \ 8.4521 \doteq 74.0951 \doteq 74.095 \ \text{cm}^2

Try another example


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




Tips to related online calculators
Tip: Our volume units converter will help you with the conversion of volume units.
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:


 

 

 

Next similar math problems:

  1. Hexagonal pyramid
    hexagonal-pyramid 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.
  2. 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.
  3. 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.
  4. Top of the tower
    veza The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joint
  5. Pyramid 4sides
    pyramid_2 Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
  6. Triangular pyramid
    tetrahedron1 Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
  7. Triangular pyramid
    trojboky_ihlan Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
  8. Regular quadrilateral pyramid
    pyramid_3 Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm.
  9. Pyramid height
    pyramid333 Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.
  10. 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?
  11. Octahedron
    octahedron All walls of regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron.
  12. Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  13. Theorem prove
    thales_1 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?
  14. 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
  15. Reference angle
    anglemeter Find the reference angle of each angle:
  16. Double ladder
    rr_rebrik The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
  17. Double ladder
    dvojak The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?