Question

The surface area of a regular octahedron is $150\sqrt{3}sq.cm$. The volume of the octahedron (in cu. cm) will be

• A. $648\sqrt{6}$
• B. $515\sqrt{6}$
• C. $343\sqrt{6}$
• D. $125\sqrt{6}$

Answer 1

Answer: (D)

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
$V=\frac{\sqrt{2}}{3}{a}^3=\frac{\sqrt{2}}{3}(5\sqrt{3}{)}^3$
$=\frac{\sqrt{2}}{3}\times 125\times 3\sqrt{3}$
$=125\sqrt{6}cu.cm$