Answer:
Solution :
Here we have given that the all edges if octahedron are 10 cm. We need to find the volume of regular octahedron.
[tex] \rule{300}{1.5}[/tex]
As we know that the formula of volume of octahedron is :
[tex]\longrightarrow{\pmb{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} {a}^{3}}}}[/tex]
Substituting all the given values in the formula to find the volume of regular octahedron :
[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} {a}^{3}}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} \times {(10)}^{3}}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} \times {(10 \times 10 \times 10)}}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} \times {(1000)}}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} \times 1000}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{ \sqrt{2} }{3} \times 1000}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = 0.471404 \times 1000}}}[/tex]
[tex]{\longrightarrow{\sf{\underline{\underline{\red{Volume_{(Octahedron)} \approx 471.404 \: {cm}^{3}}}}}}}[/tex]
Hence, the volume of regular octahedron is 471.404 cm³.
[tex] \rule{300}{1.5}[/tex]
