Question

A regular hexagon of side $2cm$ is inscribed in a circle of radius $r$. If $\frac{7}{r^2}+\frac{3}{r^3}=k$, then $k$= ?

Answer 1

In a Regular hexagon with side $2cm$ the circle circumscribing it also has $2cm$

$⟹r=2cm$

$\frac{7}{2^2}+\frac{3}{2^3}$
$\frac{7}{4}+\frac{3}{8}$
$\frac{14+3}{8}=\frac{17}{8}=2\frac{1}{8}$

$k=2\frac{1}{8}$