A hemispherical dome is open from its base and is made of iron. Thickness of dome is 3.5 meter. Total cost of painting domes outer curved surface is Rs 2464. If the rate of painting is Rs 8 per meter$$^2$$, then what is the volume (in meter$$^3$$) of iron used in making dome?

Total cost of painting domes outer curved surface is Rs 2464. 

And the rate of painting is Rs 8 per meter$$^2$$.

So, Total curved surface area = $$\frac{2464}{8}\ m^2=308\ m^2.$$

So, $$2\pi r^2=308.$$

or, $$r^2=\frac{308}{2\pi\ }=49.0197.$$

or, $$r=7.0014.$$

So, Total Volume = $$\frac{2}{3}\pi r^3\ =\frac{2}{3}\pi\times7.0014^3=718.8086\ m^3.$$

Volume of inside = $$=\frac{2}{3}\pi\times3.5^3=89.7971\ m^3.$$

So, Volume of iron = $$\left(718.80-89.7971\right)\ m^3\simeq\ 629\ m^3.$$

D is correct choice.