'Equal' Volume and Area

Let the radius of the sphere be $R$ . Then, the volume of the sphere is $\frac {4}{3} \pi R^3$ , while the surface are is $4 \pi R^2$ . Hence, $\frac {4}{3} \pi R^3 = 4 \pi R^2$ $\Rightarrow \pi 4 R^2 ( \frac {1}{3} R - 1) = 0$ , so $R = 3$ . Hence, the volume of the sphere is $(\frac {4}{3} \pi R^3= 36 \pi$ . Hence, $N = 36$ .