Let $f(x)=\frac{x^4}{4}+\frac{1}{8x^2}$ and let $R$ be the region bounded by the graph of $f$ and the $x-$axis on the interval $1,2.$

a$.$ Find the area of the surface generated when the graph of $f$ on $1,2$ is revolved about the $x-$axis. Use technology to evaluate or approximate the integral.

b$.$ Find the length of the curve $y=f(x)$ on $1,2.$

c$.$ Find the volume of the solid generated when $R$ is revolved about the $y-$axis.

d$.$ Find the volume of the solid generated when $R$ is revolved about the $x-$axis. Use technology to evaluate or approximate the integral.