Hexa pyramid

The base of the regular pyramid is a hexagon, which can be described by a circle with a radius of 1 m. Find the volume of the pyramid 2.5 m high.

Correct answer:

V =  2.1651 m³

Step-by-step explanation:

$$\begin{gathered} r=1\text{ m } \\ h=2.5\text{ m } \\ {S}_1={\displaystyle \frac{\sqrt{3}}{4}}\cdot r^2={\displaystyle \frac{\sqrt{3}}{4}}\cdot 1^2\doteq 0.433{\text{m}}^2 \\ S=6\cdot S_1=6\cdot 0.433\doteq 2.5981{\text{m}}^2 \\ V={\displaystyle \frac{1}{3}}\cdot S\cdot h={\displaystyle \frac{1}{3}}\cdot 2.5981\cdot 2.5=2.1651{\text{m}}^3 \end{gathered}$$

Try another example

Related math problems and questions:

• 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.
• 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
  Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
• Hexagon 5
  The distance of parallel sides of regular hexagonal is 61 cm. Calculate the length of the radius of the circle described to this hexagon.
• Rectangular base pyramid
  Calculate an area of the shell of the pyramid with a rectangular base of 2.8 m and 1.4 m and height 2.5 meters.
• Hexagon A
  Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
• Octagonal pyramid
  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°.
• Roof 8
  How many liters of air are under the roof of the tower, which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof.
• 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.
• 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.
• Office
  Office building was built in the shape of a regular hexagon inscribed in a circle with a radius of 12 m. The height of the walls is 7m. How much CZK cost plastering the walls of the building, if per 1 m square cost CZK 400?
• Hexaprism container
  Calculate the volume and surface in the shape of a regular hexagonal prism with a height of 1.4 m with a base edge of 3dm and a corresponding height of 2.6 dm.
• 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.
• Flowerbed
  Flowerbed has the shape of a truncated pyramid, the bottom edge of the base a = 10 m, the upper base b = 9 m. Deviation angle between edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be planted if 1 m² =
• Pentagonal prism
  The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism.
• Glass
  How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?
• Triangular pyramid
  Calculate the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height v = 20cm.