We have been given that segment KL is a diameter of circle Q. Circle Q is represented by the equation [tex]\left(x-11\right)^2+\left(y+15\right)^2=7[/tex]. We are asked to find the length of KL.
We know that standard equation of a circle is in form [tex]\left(x-h\right)^2+\left(y-k\right)^2=r^2[/tex], where point (h,k) represents center of circle and r represents radius of circle.
Upon comparing our given equation with standard equation of circle, we can see that the center of the circle is at point [tex](11,-15)[/tex] and [tex]r^2=7[/tex].
Let us solve for r by taking positive square root.
[tex]\sqrt{r^2}=\sqrt{7}[/tex]
[tex]r=\sqrt{7}[/tex]
We know that diameter is two times radius, so value of diameter KL would be 2 times r.
[tex]KL=2\cdot \sqrt{7}[/tex]
Therefore, the volume of KL is [tex]2\sqrt{7}[/tex] and option C is the correct choice.
