Multiple choice

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

  1. $2\dfrac 18$
  2. $6\dfrac 18$
  3. $\dfrac 18$
  4. $3\dfrac 18$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a regular hexagon of side s = 2, the circumradius r = s = 2. Substituting r = 2 into the expression: 7/(2^2) + 3/(2^3) = 7/4 + 3/8 = 14/8 + 3/8 = 17/8 = 2 1/8.

AI explanation

For a regular hexagon inscribed in a circle, the radius of the circle is equal to the side length of the hexagon. Therefore, the radius r is 2 cm. Substituting r equals 2 into the expression for k, we get seven divided by two squared plus three divided by two cubed. This simplifies to seven divided by 4 plus three divided by 8, which is fourteen divided by 8 plus three divided by 8. The sum is seventeen divided by 8, which equals 2 and one-eighth.

Keep practicing — related questions