How do I find the volume of a dodecahedron?

How do I find the volume of a dodecahedron?

Volume of a Dodecahedron

  1. First, find the square root of 5, which is 2.236.
  2. Multiply that by 7, which gives you 15.652.
  3. Add 15 to get 30.652.
  4. Divide the above sum by 4, which gives you 7.663.
  5. Now, multiply the above answer by e cubed. (Remember that e is 6, so e cubed is 216.) So, 7.663 x 216 = 1655.208.

What is a 12 sided 3d shape called?

In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka “twelve” + ἕδρα hédra “base”, “seat” or “face”) or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid.

What is a 20 sided 3d shape called?

The icosahedron – 20-sided polyhedron – is frequent. Most often each face of the die is inscribed with a number in Greek and/or Latin up to the number of faces on the polyhedron.

Can dodecahedron fill space?

The rhombic dodecahedron can be used to tessellate three-dimensional space: it can be stacked to fill a space, much like hexagons fill a plane. This polyhedron in a space-filling tessellation can be seen as the Voronoi tessellation of the face-centered cubic lattice.

How do u find the area of a decagon?

The formula to determine the value of the area of a decagon is 5a2/2 × √5+2√5 5 + 2 5 , where ‘a’ is the side length of the decagon.

What is the volume of a icosahedron?

Another way to calculate the volume is divide the icosahedron into 3 parts. The height of the pyramid is calculated by the Pythagoras theorem. h² = r² + a². The bottom part of the icosahedron is the same.

What is a 100 sided 3d shape called?

Zocchihedron is the label of a 100-sided die, a 3d shape. If a 3d shape with 100 faces is called hecatohedron. In case of two dimensional shapes, a shape with 100 sides is called Hectogon. The relationship between the number of faces, edges and vertices of a 3d shape is given by: F + V = E + 2.

Do octahedrons pack?

Its volume can be calculated knowing the volume of an octahedron. It is a space-filling polyhedron. These polyhedra pack together to fill space, forming a 3 dimensional space tessellation or tilling.

Do tetrahedra fill space?

A space-filling polyhedron, sometimes called a plesiohedron (Grünbaum and Shephard 1980), is a polyhedron which can be used to generate a tessellation of space. Although even Aristotle himself proclaimed in his work On the Heavens that the tetrahedron fills space, it in fact does not.

What is the formula for area of a dodecagon?

The formula for finding the area of a regular dodecagon is: A = 3 × ( 2 + √3 ) × s2 , where A = the area of the dodecagon, s = the length of its side. For example, if the side of a regular dodecagon measures 8 units, the area of this dodecagon will be: A = 3 × ( 2 + √3 ) × s2 .

How do you calculate the volume of a donut?

The volume of a torus is calculated by multiplying the area of the cross-section by the circumference of the ring. Volume = π × r2 × 2 × π × R.