Answer
$(x-3)^3+(y-2)^2+(z-7)^2=11$
Work Step by Step
By Exercise 19(a), the midpoint of the diameter (and thus the center of the sphere) is (3,2,7). The radius is half the diameter, so $r=\frac{1}{2} \sqrt{(4-2)^2+(3-1)^2+(10-4)^2}= \frac{1}{2} \sqrt{44}=\sqrt{11}$. Therefore an equation of the sphere is $(x-3)^3+(y-2)^2+(z-7)^2=11$.
