Hexagonal pyramid

Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm.

Correct answer:

V =  1995.3225 cm³

Step-by-step explanation:

$$\begin{gathered} a=12\text{ cm } \\ s=20\text{ cm } \\ {S}_0=\sqrt{3}\mathrm{/}4\cdot a^2=\sqrt{3}\mathrm{/}4\cdot 12^2=36\sqrt{3}{\text{cm}}^2\doteq 62.3538{\text{cm}}^2 \\ {S}_1=6\cdot S_0=6\cdot 62.3538=216\sqrt{3}{\text{cm}}^2\doteq 374.123{\text{cm}}^2 \\ {s}^2=h^2+a^2 \\ h=\sqrt{s^2-a^2}=\sqrt{20^2-12^2}=16\text{ cm } \\ V={\displaystyle \frac{1}{3}}\cdot S_1\cdot h={\displaystyle \frac{1}{3}}\cdot 374.123\cdot 16=1995.3225{\text{cm}}^3 \end{gathered}$$

Try another example

Related math problems and questions:

• Hexagonal 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.
• Wall height
  Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height w = 20 cm.
• 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.
• 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.
• Hexagonal pyramid
  Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm.
• Pentagonal pyramid
  The height of a regular pentagonal pyramid is as long as the edge of the base, 20 cm. Calculate the volume and surface area of the pyramid.
• Regular hexagonal prism
  Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.
• Hexagonal pyramid
  Find the area of a shell of the regular hexagonal pyramid, if you know that its base edge is 5 cm long and the height of this pyramid is 10 cm.
• 9-gon pyramid
  Calculate the volume and the surface of a nine-sided pyramid, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm.
• Hexagonal pyramid
  Calculate the volume and surface area of a regular hexagonal pyramid with a base edge a = 30 m and a side edge b = 50 m.
• Pyramid height
  Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.
• Hexagon cut pyramid
  Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge is 12 cm, and the side edge length is 41 cm.
• Tetrahedral pyramid
  A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area).
• Hexagon
  Calculate the regular hexagonal prism's surface whose base edge a = 12cm and side edge b = 3 dm.
• Triangular pyramid
  It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm³. What is it content (surface area)?
• Triangular pyramid
  Calculate the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height v = 20cm.
• Quadrilateral pyramid
  In a regular quadrilateral pyramid, the side edge is e = 7 dm, and the diagonal of the base is 50 cm. Calculate the pyramid shell area.