The center of the sphere is $\left(\cos 46°,\sin 46°\right)$ and a point on the surface of the sphere is $\left(-\sin 46°,\cos 46°\right)$ , then the volume of sphere is

Given, Center of the sphere $=A\left(\cos 46°,\sin 46°\right)$

Point of the sphere $=B\left(-\sin 46°,\cos 46°\right)$

Distance between $A,B$  is equal to radius of sphere

$AB=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

$r=\sqrt{{\left(\cos 46+\sin 46\right)}^2+{\left(\sin 46-\cos 46\right)}^2}$

$=\sqrt{{\cos }^{2}46°+{\sin }^{2}46°+2\cdot \cos 46°\cdot \sin 46°+{\sin }^{2}46°+{\cos }^{2}46°-2\cos 46°\cdot \sin 46°}$

$r=\sqrt{1+1}=\sqrt{2}$

Volume of sphere $\left(v\right)=\frac{4}{3}\pi r^3$

$=\frac{4}{3}\pi {\left(\sqrt{2}\right)}^3$

$=\frac{4}{3}\pi 2\sqrt{2}$

$=\frac{8\sqrt{2}\pi }{3}$ .