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Let $f$ be the function given by $f(x)=4 x^{2}-$ $x^{3}$, and let $\ell$ be the line $y=18-3 x$, where $\ell$ is tangent to the graph of $f$. Let $R$ be the region bounded by the graph of $f$ and the $x$ axis, and let $f(x)=4 x^{2}-$$0$ be the region bounded by the graph of $f$, the line $\ell$, and the $x$-axis, as shown.$\newline$(a) Show that $\ell$ is tangent to the graph of $f(x)=4 x^{2}-$$5$ $f(x)=4 x^{2}-$$6$ at the point $f(x)=4 x^{2}-$$7$.$\newline$(b) Find the area of $f(x)=4 x^{2}-$$0$.$\newline$(c) Find the volume of the solid generated when $R$ is revolved about the $x$-axis.