Answer
$(x-3)^2+(y-8)^2+(z-1)^2=30$
Work Step by Step
First, determine the radius of the sphere using the distance formula:
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$
$r=\sqrt{(3-4)^2+(8-3)^2+(1+1)^2}=\sqrt{30}$
The equation for a sphere is represented by:
$(x-h)^2+(y-k)^2+(z-l)^2=r^2$
in which the point $(h,k,l)$ is the center of the sphere and $r$ is the radius.
Plug in the values for the center and the radius.
$(x-3)^2+(y-8)^2+(z-1)^2=30$
