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Q.
The surface area of a regular octahedron is $150 \sqrt{3} sq . cm$. The volume of the octahedron (in cu. cm) will be
Mensuration
Solution:
Surface area of a regular octahedron is $150 \sqrt{3}$ sq. cm.
$2 \sqrt{3} a^2=150 \sqrt{3} $
$a=\sqrt{75}=5 \sqrt{3} cm$
Volume of the octahedron
$V=\frac{\sqrt{2}}{3} a^3=\frac{\sqrt{2}}{3}(5 \sqrt{3})^3 $
$=\frac{\sqrt{2}}{3} \times 125 \times 3 \sqrt{3} $
$=125 \sqrt{6} cu . cm$