Regular hexagonal prism

Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.

Correct answer:

V =  2636.7965 cm3

Step-by-step explanation:

u=24 cm v=25 cm  u1=2a  (u2/2)2+(a/2)2=a2 u22/4+a2/4=a2 u22/4+=3/4 a2  u2=3 a  h2+u12=v2 h2+u22=u2  h2+(2a)2=v2 h2+(3 a)2=u2 4a23a2=v2u2 a2=v2u2 a=v2u2=252242=7 cm  h=v24 a2=2524 72=429 cm20.7123 cm  S1=3 a24=3 72421.2176 cm2 S=6 S1=6 21.2176127.3057  V=S h=127.3057 20.7123=2636.7965 cm3



We will be pleased if You send us any improvements to this math problem. Thank you!



avatar




Tips to related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.
Tip: Our volume units converter will help you with the conversion of volume units.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions:

  • Hexagonal pyramid
    hexa_pyramid Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm.
  • Quadrangular prism
    hranol4sreg_7 Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.
  • Hexagonal prism 2
    hranol6b The regular hexagonal prism has a surface of 140 cm2 and height of 5 cm. Calculate its volume.
  • Cuboid diagonals
    kvadr_diagonal The cuboid has dimensions of 15, 20 and 40 cm. Calculate its volume and surface, the length of the body diagonal and the lengths of all three wall diagonals.
  • Four sided prism
    hranol4sreg 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.
  • Hexagonal pyramid
    hexa_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.
  • Triangular prism
    prism3_1 The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm3? And the surface cm2?
  • Triangular prism - regular
    prism3s The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism.
  • 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.
  • Ratio of edges
    diagonal_2 The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
  • Cube diagonals
    cube_diagonals_4 Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
  • Diagonals of the rhombus
    kosostvorec_3 How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm2?
  • Block or cuboid
    cuboid The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
  • Cube diagonals
    krychlicka_1 Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
  • The regular
    hranol3b 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.
  • Quadrilateral prism
    hranol 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.
  • Nice prism
    diagonal_rectangular_prism.JPG Calculate the cuboid's surface if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.