How to Calculate the Volume of a Regular Octahedron

Step-by-Step Guide

1. 1

   Step 1: Remember or write down the formula V=23a3{\displaystyle V={\frac {\sqrt {2}}{3}}a^{3}}.

     It is the formula for the volume of a regular octahedron. ,  Look at the picture for help.
   
   Example:
   If you're given a=4{\displaystyle a=4}, you can plug it in as V=23a3=23(43){\displaystyle V={\frac {\sqrt {2}}{3}}a^{3}={\frac {\sqrt {2}}{3}}(4^{3})} ,  Note that √2 is similar to
   1.41.
   
   Example:
   V=23(43)=1.413(43)=0.47(43){\displaystyle V={\frac {\sqrt {2}}{3}}(4^{3})={\frac {1.41}{3}}(4^{3})=0.47(4^{3})} , Example:
   V=0.47(43)=0.47(64){\displaystyle V=0.47(4^{3})=0.47(64)} , Example:
   V=0.47(64)=30.08{\displaystyle V=0.47(64)=30.08}.
   
   V{\displaystyle V} is roughly
   30.08.
2. 2

   Step 2: Find the value of the side length and replace a{\displaystyle a}.

3. 3

   Step 3: Using the order of operations

4. 4

   Step 4:  divide √2 by 3.

5. 5

   Step 5: Cube a{\displaystyle a}

6. 6

   Step 6: Multiply the quotient by the product.

Detailed Guide

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