Hexa prism

Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm.

Correct answer:

V =  1163.9381 cm³

Step-by-step explanation:

$$\begin{gathered} a=4\text{ cm } \\ v=28\text{ cm } \\ {S}_1={\displaystyle \frac{\sqrt{3}}{4}}\cdot a^2={\displaystyle \frac{\sqrt{3}}{4}}\cdot 4^2=4\sqrt{3}{\text{cm}}^2\doteq 6.9282{\text{cm}}^2 \\ S=6\cdot S_1=6\cdot 6.9282=24\sqrt{3}{\text{cm}}^2\doteq 41.5692{\text{cm}}^2 \\ V=v\cdot S=28\cdot 41.5692=1163.9381{\text{cm}}^3 \end{gathered}$$

Try another example

Related math problems and questions:

• Right-angled triangle base
  Find the volume and surface area of a triangular prism with a right-angled triangle base if the length of the prism base legs are 7.2 cm and 4.7 cm and the height of a prism is 24 cm.
• Hexagonal prism
  The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Find the volume and surface of the prism.
• Four sided prism
  Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50-degree angle with the base plane.
• The regular
  The regular triangular prism has a base in the shape of an isosceles triangle with a base of 86 mm and 6.4 cm arms, the height of the prism is 24 cm. Calculate its volume.
• Triangular prism
  Calculate the surface of a regular triangular prism, the edges of the base are 6 cm long and the height of the prism is 15 cm.
• Triangular prism
  The base of the perpendicular triangular prism is a right triangle with a leg length of 5 cm. The content area of the largest sidewall of its surface is 130 cm², and the height of the body is 10 cm. Calculate its volume.
• Prism - eq triangle
  Calculate the volume and surface of the prism with the base of an equilateral triangle with side a = 4cm and the body height is 6cm.
• Base of prism
  The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm².
• Prism
  Right-angled prism, whose base is a right triangle with leg a = 3 cm and hypotenuse c = 13 cm, has the same volume as a cube with an edge length of 3 dm. a) Find the height of the prism b) Calculate the surface of the prism c) What percentage of the cube'
• Pyramid 4sides
  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.
• Prism
  The base of a perpendicular triangular prism is a right triangle with legs 4.5 cm and 6 cm long. What is the surface of the prism, if its volume is 54 cubic centimeters?
• Vertical prism
  The base of the vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism
• Prism
  Calculate the volume of the rhombic prism. The prism base is a rhombus whose one diagonal is 47 cm, and the edge of the base is 28 cm. The edge length of the base of the prism and height is 3:5.
• Prism 4 sides
  The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters
• 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.
• Quadrilateral prism
  The height of a regular quadrilateral prism is v = 10 cm, the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the volume of the prism.
• Triangular prism
  Calculate the volume and surface area of a triangular prism if it is given: a = 6.8 dm. ..Va = 4 dm. (base edge length and base triangle height length) ... ... .v = 23 dm (body height)