An octahedron is a form that is developed by joining by 2 pyramids in ~ its bases. As soon as joined the form converts come 8 faced, 12 edges, and also 6 vertices. One octahedron is most typically known as the regular octahedron i.e. As soon as all the encounters are of the exact same shape and also size. Yet in many cases, the is not important that all faces have to it is in the very same to be referred to as an octahedron, with the very same size also, the shape is still referred to as octahedron. Let us learn more about the meaning, properties, area, and volume recipe of one octahedron.
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|1.||Meaning of Octahedron|
|2.||Properties of one Octahedron|
|3.||Surface Area of an Octahedron|
|4.||Volume of one Octahedron|
|5.||FAQs top top Octahedron|
Meaning the Octahedron
The indigenous octahedron is derived from the Greek indigenous 'Oktaedron' which means 8 faced. One octahedron is a polyhedron v 8 faces, 12 edges, and also 6 vertices and at each vertex 4 edge meet. It is among the five platonic solids with encounters that room shaped prefer an it is provided triangle.
Properties of one Octahedron
Mentioned below are a couple of properties of an octahedron:An octahedron has actually 12 edges.In a regular octahedron, the angles between the edges are measured at 60° but the dihedral angle is measured in ~ 109.28°.
Surface Area of one Octahedron
A constant octahedron is made up of 8 it is provided sides. The area of an octahedron is 2 multiplied by the square that the length of one edge multiplied by the square root of three. Allow us discover out the formula because that calculating the surface ar area of one octahedron. Permit the size of every side of the octahedron be 'a'. Since the area that an equilateral triangle is = (√3/4) × side2,
Area the one side of the octahedron = Area of an it is provided triangle = (√3/4) × a2
Hence, Area the the octahedron = 8 × (√3/4) × a2 = 2 ×√3 × a2
Therefore, Surface Area (A) = 2 ×√3 × a2
Volume of an Octahedron
An octahedron can be separated into two pyramids which way the volume of an octahedron is twice the moment of the volume that a pyramid. To find the volume of an octahedron, we can find the volume of one pyramid and then calculation it for two pyramids or an octahedron.
The volume the the pyramid = (Base area × Height)/3
The base of the pyramid is a square, hence base area = a2
Height the the pyramid (H) = \(\sqrta^2 - (\frac a\sqrt2)^2\)
The volume that the pyramid = \(\dfraca^2 \times \sqrta^2 - (\frac a\sqrt2)^23 = \dfrac a^33 \sqrt2\)
Hence, volume of the octahedron = 2 × volume the the pyramid = 2 × (a3)/3√2 =√2/3 × a3
Volume (V) = √2/3 × a3
Related short articles on Octahedron
Listed below are a couple of interesting topics the are related to the principle of one octahedron. Let's have actually a look:
Examples ~ above Octahedron
Example 1: Yasmin has actually a pair the earrings that room shaped choose an octahedron. She desires to recognize the surface ar area of every earring. Deserve to you find the surface area if the size of the earring is 0.4 in?
Surface area (A) of one octahedron = 2 ×√3 × a2
Given, a = 0.4 in
Hence, surface area that earring = 2 × √3 × (0.4)2
Therefore, surface area of the earrings = 0.5542 in2
Example 2: Sean wants to uncover the volume the a dice shaped choose an octahedron through a next of length 1.7 in. Can you assist him with this?
Volume (V) = (√2/3)× a3
Given, a = 1.7 in
Hence, Volume the the dice = √2/3 × 1.73
Therefore, Volume that the dice = 2.31567 in3
Example 3: A cable of length 60 ft is bending to form a constant octahedron. Uncover the length of each of the edges of the octahedron.
Given, the size of the cable = 60 ft. We recognize that an octahedron has 12 edges. Hence, the length of each edge the the octahedron = 60/12 = 5 ft.
Therefore, length of every edge of the octahedron = 5 ft
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FAQs ~ above Octahedron
Is Octahedron a Prism?
No, one octahedron is not a prism. An octahedral prism is do of 2 octahedra that are linked to each other via 8 triangle prisms.
Is Octahedron a Pyramid?
Octahedron is a 3-dimensional geometric form that is developed by joining the bases that 2 pyramids make it right into a form with 8 faced, 12 edges, and 6 vertices. The triangle pyramids deserve to be taken into consideration as the faces of the octahedron.
How countless Vertices does an Octahedron have?
An octahedron has actually 6 vertices out of which 4 vertices space there top top the square base, 1 peak on the top, and 1 at the bottom.
Does an Octahedron have Hexagonal Faces?
No, an octahedron does not have hexagonal faces but rather has actually triangular faces. A continuous octahedron has actually equilateral triangle faces.
What is a continual Octahedron?
A continuous octahedron has all it is intended triangular encounters of same length. It is a rectified version of a tetrahedron and also is taken into consideration the double polyhedron the a cube. In a constant octahedron, all encounters are the exact same size and also shape. It is formed by joining 2 equally sized pyramids at their base.
See more: Greatest Common Factor Of 4 And 12 ? Gcf Of 4 And 12
What space the various Parts of one Octahedron?
An octahedron is do of different parts together as:Face: one octahedron consists of 8 faces that room shaped choose a triangleBase: one octahedron has actually a square-shaped baseEdge: an octahedron is composed of 12 edgesVertex: one octahedron consists of 6 vertices and each crest is developed when 4 edge intersect.