= Solution
{c}
Interpolate the <radius> and height by
$$
\rho(t)=a+(c-a)t,\qquad z(t)=b+(d-b)t,\qquad 0\leq t\leq1.
$$
A <parametrized surface> for the <conical frustum> is
$$
\boxed{\mathbf R(t,\theta)=\bigl(\rho(t)\cos\theta,\rho(t)\sin\theta,b+(d-b)t\bigr),\quad 0\leq t\leq1,\quad0\leq\theta<2\pi.}
$$
The strict positivity of $a,c$ gives $\rho(t)>0$. Since $d>b$, the height identifies $t$ uniquely; the <angle> then identifies a <point> of each <circle> uniquely modulo $2\pi$. Hence this covers the lateral <surface of revolution> once. If $a=c$, it is the lateral surface of a <circular cylinder>.
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