Question

How do I solve this math word problem?

Answer 1

A)

$\bf A=\pi r^2\qquad r=1.5t\implies A(t)=\pi (1.5t)^2\implies A(t)=(1.5^2t^2)\pi \\\\\\ \boxed{A(t)=2.25t^2\pi }\qquad t=3\implies A(3)=2.25(3)^2\pi$

b)

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