a)
[tex]\bf A=\pi r^2\qquad r=1.5t\implies A(t)=\pi (1.5t)^2\implies A(t)=(1.5^2t^2)\pi
\\\\\\
\boxed{A(t)=2.25t^2\pi }\qquad t=3\implies A(3)=2.25(3)^2\pi [/tex]
b)
[tex]\bf \textit{ratio of the height to radius}\implies \cfrac{16}{8}\iff\cfrac{2}{1}\implies 2
\\\\\\
h=2r
\\\\\\
V=\cfrac{\pi r^2 h}{3}\qquad
\begin{cases}
r=1.5t\\
h=2r\\
\qquad 2(1.5t)\\
\qquad 3t
\end{cases}\implies V(t)=\cfrac{\pi \cdot (1.5t)^2\cdot 3t}{3}
\\\\\\
V(1)=\cfrac{\pi \cdot [1.5(1)]^2\cdot 3(1)}{3}[/tex]
